Find the definite integral of ʃπ/20 cos x + sin x dx​

1. Find the definite integral of ʃπ/20 cos x + sin x dx​

Integral~

the definite integral of ʃπ/20 cos x + sin x dx​

is

[tex]\boxed{\sf{=\frac{\pi\sin\left(x\right)}{20}-\cos\left(x\right)+C}}[/tex]

[tex] \: [/tex]

Pendahuluan

[tex]\boxed{\boxed{\mathbf{A.}} \ \boxed{\mathbf{Pengertian \ Singkat}}}[/tex]

Integral => lawan dari turunan. Jika f(x) turunan pertama dari F(x), maka :

[tex]\boxed{\mathbf{\int_{ }^{ }f\left(x\right)dx=F\left(x\right)+C}}[/tex]

Rumus yang sering dipakai :

[tex]\boxed{\mathbf{\int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C}}[/tex]

[tex] \: [/tex]

[tex]\boxed{\boxed{\mathbf{B.}} \ \boxed{\mathbf{Integral \ Tak \ Tentu}}}[/tex]

ada 6 integral tak tentu yang perlu anda ketahui, diantaranya :

[tex]\mathbf{1.\ \ \int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C;n\ne1}[/tex]

[tex]\mathbf{2.\ \ \int_{ }^{ }\frac{1}{x}\ dx=\ln\ | x |+C}[/tex]

[tex]\mathbf{3.\ \ \int_{ }^{ }\sin x\ dx=-\cos x+C}[/tex]

[tex]\mathbf{4.\ \ \int_{ }^{ }\cos x\ dx=\sin x+C}[/tex]

[tex]\mathbf{5.\ \ \int_{ }^{ }e^{x}\ dx=e^{x}+C}[/tex]

[tex]\mathbf{6.\ \ \int_{ }^{ }a^{x}\ dx=\frac{a^{x}}{\ln a}+C}[/tex]

[tex] \: [/tex]

[tex]\boxed{\boxed{\mathbf{C.}} \ \boxed{\mathbf{Integral \ Tentu}}}[/tex]

ada 6 integral tentu juga yang perlu anda pahami, diantaranya :

[tex]\mathbf{1.\ \ \int_{a}^{b}kf\left(x\right)dx=k\int_{a}^{b}f\left(x\right)dx}[/tex]

[tex]\footnotesize\mathbf{2.\ \ \int_{a}^{b}f\left(x\right)\pm g\left(x\right)dx=\int_{a}^{b}f\left(x\right)dx\pm\int_{a}^{b}g\left(x\right)dx}[/tex]

[tex]\mathbf{3.\ \ \int_{a}^{b}f\left(x\right)\ dx=-\int_{b}^{a}f\left(x\right)\ dx}[/tex]

[tex]\small\mathbf{4.\ \ \int_{a}^{b}f\left(x\right)dx+\int_{b}^{c}f\left(x\right)dx=\int_{a}^{c}f\left(x\right)dx}[/tex]

[tex]\mathbf{5.\ \ \int_{a}^{a}f\left(x\right)\ dx=0}[/tex]

[tex]\footnotesize\mathbf{6.\ \ \int_{a}^{b}f\left(x\right)dx=\int_{a+k}^{b+k}f\left(x-k\right)dx=\int_{a-k}^{b-k}f\left(x+k\right)dx}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

Pembahasan

Diketahui :

[tex]\large\sf{\int_{ }^{ }(\frac{\pi}{20}\cos (x)+\sin (x)) \ dx}[/tex]

Ditanya :

hasil dari integral tersebut?

Jawaban :

[tex]\large\sf{\int_{ }^{ }(\frac{\pi}{20}\cos (x)+\sin (x)) \ dx}[/tex]

[tex]\large\sf{\frac{\pi}{20}\int_{ }^{ }\cos (x) \ dx +\int_{ }^{ }\sin (x) \ dx }[/tex]

[tex]\large\boxed{\sf{=\frac{\pi\sin\left(x\right)}{20}-\cos\left(x\right)+C}}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

Pelajari Lebih Lanjut :Contoh soal integral tentu (1) : brainly.co.id/tugas/50510100Contoh soal integral tentu (2) : brainly.co.id/tugas/50454066Tentukan ∫(2x^{2} + 5x)^{2} dx : brainly.co.id/tugas/50364777Integral dari (x^3 +√x) dx : https://brainly.co.id/tugas/50722822

[tex] \: [/tex]

[tex] \: [/tex]

Detail Jawaban :

Kelas : 12 SMA

Bab : 1

Sub Bab : Bab 1 - Integral

Kode kategorisasi : 12.2.1

Kata Kunci : Integral tak tentu.

2. INTEGRAL OF THE DAY - QUIZ #20Tentukan hasil dari :[tex] \displaystyle \int^{ \frac{ \pi}{3}}_{ \frac{\pi}{12}} \frac{ \cos(x) +(2 + \sqrt{3} ) \sin(x) }{2 + \sqrt{3} } \cdot \sin(x) \: \sf {dx} [/tex]golden hint : (2 + √3) = tan (π/3 + π/12)​

[tex]\int \cos~x.\sin~x~dx[/tex]

[tex]=\int \left(\frac{1}{2}\times 2.\cos~x.\sin~x\right)~dx[/tex]

[tex]=\frac{1}{2}~\int \sin~2x~dx[/tex]

[tex]\boxed{\boxed{\int \cos~x.\sin~x~dx=-\frac{1}{4}\cos~2x+c}}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\int \sin^2~x~dx[/tex]

[tex]=\int \left(\frac{1}{2}\times (1-\cos~2x)\right)~dx[/tex]

[tex]\boxed{\boxed{\int \sin^2~x~dx=\frac{1}{2}\left(x-\frac{1}{2}.\sin~2x\right)+c}}[/tex]

••••••••••••••••••••••••••••••••••••••••••••••••••

[tex]\int \limits_\frac{\pi}{12}^\frac{\pi}{3} \left(\frac{\cos~x~+~\left(2~+~\sqrt{3}\right).\sin~x}{2~+~\sqrt{3}}.\sin~x\right)~dx[/tex]

[tex]\begin{array}{ll}=&\frac{1}{2~+~\sqrt{3}}.\int \limits_\frac{\pi}{12}^\frac{\pi}{3} (\cos~x.\sin~x)~dx\\&+~\int \limits_\frac{\pi}{12}^\frac{\pi}{3} \sin^2~x~dx\\~\\=&\frac{1}{2~+~\sqrt{3}}.\left[-\frac{1}{4}\cos~2x\right]_\frac{\pi}{12}^\frac{\pi}{3}\\&+~\left[\frac{1}{2}\left(x-\frac{1}{2}.\sin~2x\right)\right]_\frac{\pi}{12}^\frac{\pi}{3}\\~\\=&\frac{1}{2~+~\sqrt{3}}.\left[-\frac{1}{4}.\cos~\frac{2\pi}{3}-\left(-\frac{1}{4}.\cos~\frac{\pi}{6}\right)\right]\\&+\left[\frac{1}{2}\left(\frac{\pi}{3}-\frac{1}{2}.\sin~\frac{2\pi}{3}\right)\right.\\&\left.-\left(\frac{1}{2}\left(\frac{\pi}{12}-\frac{1}{2}.\sin~\frac{\pi}{6}\right)\right)\right]\\~\\=&\frac{1}{2~+~\sqrt{3}}.\left[\left(-\frac{1}{4}\right).\left(-\frac{1}{2}\right)-\left(-\frac{1}{4}\right).\left(\frac{1}{2}\sqrt{3}\right)\right]\\&+\left[\frac{1}{2}\left(\frac{\pi}{3}-\frac{1}{2}.\left(\frac{1}{2}\sqrt{3}\right)\right)\right.\\&\left.-\left(\frac{1}{2}\left(\frac{\pi}{12}-\frac{1}{2}.\left(\frac{1}{2}\right)\right)\right)\right]\\~\\=&\frac{1}{2~+~\sqrt{3}}.\left[\frac{1}{8}+\frac{1}{8}\sqrt{3}\right]\\&+\left[\frac{1}{2}\left(\frac{\pi}{3}-\frac{1}{4}\sqrt{3}\right)\right.\\&\left.-\left(\frac{1}{2}\left(\frac{\pi}{12}-\frac{1}{4}\right)\right)\right]\\~\\=&\frac{1+\sqrt{3}}{8\left(2+\sqrt{3}\right)}+\frac{\pi}{6}-\frac{1}{8}\sqrt{3}\\&-\frac{\pi}{24}+\frac{1}{8}\\~\\=&\frac{1+\sqrt{3}}{8\left(2+\sqrt{3}\right)}+\frac{1}{8}\left(\pi+1-\sqrt{3}\right)\\~\\=&\frac{1+\sqrt{3}+\left(2+\sqrt{3}\right)\left(\pi+1-\sqrt{3}\right)}{8\left(2+\sqrt{3}\right)}\\~\\=&\frac{\left(2+\sqrt{3}\right)\pi}{8\left(2+\sqrt{3}\right)}~+~\frac{1+\sqrt{3}+\left(2+\sqrt{3}\right)\left(1-\sqrt{3}\right)}{8\left(2+\sqrt{3}\right)}\end{array}[/tex]

[tex]\boxed{\boxed{\red{\begin{array}{c}\int \limits_\frac{\pi}{12}^\frac{\pi}{3} \left(\frac{\cos~x~+~\left(2~+~\sqrt{3}\right).\sin~x}{2~+~\sqrt{3}}.\sin~x\right)~dx\\~\\\huge{=\frac{\pi}{8}}\end{array}}}}[/tex]

3. Thankfully, there is no school for sloths. Even if it exists, all the students will just sleep. These tree-dwellers spend 20 hours of their day just to sleep. When they are awake, sloths move very slowly and sluggishly. They got the name sloth from deadly sin of sloth from the bible, because they seem lazy, although their idleness is because of the metabolic adaptation to conserve energy. Sloths are mammals, and mainly found in tropical forests of Central and South America. They have sharp claws on their feet, sad-looking eyes, tiny ears, and furry. They weigh 3-7 kilograms and can grow to 0.6 – 0.8 meters. Sloths spend most of their time on trees and rarely come down from there. They can be aggressive, using their claws to attack when there are predators threatening their lives. Aside from that, they are peaceful creatures. What tense is used in the text?

Penjelasan:

Present simple......

4. 13. The uderlined word means....A. SipitB. GembulC. MenggemaskanD. PesekThe dialogue is for number 14!Tanti : "Where did you go for school excursion last week?"lo savnog welZulfa: "I went to Jatim Parkfor the school excursion."Slavons b onTanti: "How long did the trip take time?"annon blogZulfa: "It was about 7 hours."olanoJos 814. The dialogue above shows about ....A. Something happens in the time of the speaker speak.on 159AB. Something happens in the future.C. Something happens regularly.D. Something happens in the pastdono si prinses sis busThe text is for number 15–20!On Saturday, May 5th, Sarah invited her classmates to her birthday party. I was very excited. I went there with Pauand Tim. We wore fancy dress because it was a fancy dress party. I wore a ghost costume, Tim was Xena, the warrprincess, and Paula was a vampire.The party started at 7. First, we sang 'Happy Birthday'. Then, Sarah blew out the candles. After that, we ate some fand drink coke.Later on, we played some games. Everybody enjoyed them. We cheered so hard. I nearly lost my voice. Weplaying 'Hide and seek' when suddenly the lights went out. The girls were afraid of the dark and the boys laughed attFortunately, It didn't last long. In ten minutes, the light was on again, and we continued the games.Before the party was over, the MC announced the best costume of the party. Paula got the first prize. She lookShoxsviane AORX90Finally, my Dad arrived to take us home. I was so tired, but happy.Soy lo worlwb Sinhappy.​

Jawaban: 13. Kata yang tidak sesuai artinya ....

Sebuah panah

B. Gembul

C. Adorable

D. Pug

Dialognya untuk nomor 14!

Tanti: "Kemana Anda pergi tamasya sekolah minggu lalu?"

Sama sama

Zulfa: "Saya pergi ke Taman Jawa Timur untuk tamasya sekolah."

Slavia aktif

Tanti: "Berapa lama perjalanan itu memakan waktu?"

Blog Annon

Zulfa: "Itu sekitar 7 jam."

olano

Yos 8

14. Dialog di atas menunjukkan tentang ....

A. Sesuatu terjadi pada pembicara.

pada 159

SEBUAH

B. Sesuatu terjadi di masa depan.

C. Sesuatu terjadi secara teratur.

D. Sesuatu terjadi di masa lalu

mengenakan

o pengemudi bus prinses

Teks untuk nomor 15-20!

Pada hari Sabtu, 5 Mei, Sarah mengundang teman-teman sekelasnya ke pesta ulang tahunnya. Saya sangat bersemangat. Saya pergi ke sana bersama Pau

dan Tim. Kami mengenakan gaun mewah karena itu adalah pesta kostum. Saya mengenakan kostum hantu, Tim adalah Xena, sang warr

Putri, dan Paula adalah vampir.

Pesta dimulai pukul 7. Pertama, kami 'Selamat Ulang Tahun'. Kemudian, Sarah meniup lilin. Setelah itu, kami makan f

dan minum kokas.

Kemudian, kami memainkan beberapa game. Semua orang menikmatinya. Kami bersorak sangat keras. Aku hampir kehilangan suaraku. Kita

bermain 'Hide and seek' ketika tiba-tiba lampu padam. Gadis-gadis itu takut akan kegelapan dan anak-anak lelaki itu menertawakannya

Untungnya, itu tidak berlangsung lama. Dalam sepuluh menit, lampu menyala lagi, dan kami melanjutkan pertandingan.

Sebelum pesta selesai, MC mengumumkan kostum pesta terbaik. Paula mendapat hadiah pertama. Dia melihat

Shox

sviane A

ORX90

Akhirnya, ayah saya datang untuk membawa kami pulang. Saya sangat lelah, tetapi bahagia.

Soy lo worlwb Sin

senang

Penjelasan:

5. Tolong bantu saya untuk mentranslate ke bahasa Indonesia.Terima kasih byk 17. But if, in seeking to be justified in Christ.we jews find ourselves also Aming the sinners.Doesn't that Medan that Christ promotes sin?Absolutely not! 18. If i rebuild What i destroyed, then i really eould be a lawbreaker. 19. "For through the law i died to the law so that i might live for God. 20. I have been crucified with Christ and i no longer live, but Christ lives in me. The life I now live on the body. I live by faith in the Son of God. Who loves me and gave himself for me. 21. I do not set aside the Grace of God.For if righteousness could be gainef through the law.Chrisy did for nothing!"

Jawaban:

17. Tetapi jika kami sendiri, sementara kami berusaha untuk dibenarkan dalam Kristus ternyata adalah orang-orang berdosa, apakah hal itu berarti, bahwa Kristus adalah pelayan dosa? Sekali-kali tidak.

18. Karena, jikalau aku membangun kembali apa yang telah kurombak, aku menyatakan diriku sebagai pelanggar hukum Taurat.

19. Sebab aku telah mati oleh hukum Taurat untuk hukum Taurat, supaya aku hidup untuk Allah. Aku telah disalibkan dengan Kristus;

20. namun aku hidup, tetapi bukan lagi aku sendiri yang hidup, melainkan Kristus yang hidup di dalam aku. Dan hidupku yang kuhidupi sekarang di dalam daging, adalah hidup oleh iman dalam Anak Allah yang telah mengasihi aku dan menyerahkan diri-Nya untuk aku.

21. Aku tidak menolak kasih karunia Allah. Sebab sekiranya ada kebenaran oleh hukum Taurat, maka sia-sialah kematian Kristus.

6. 19 RomiAmanda can your answer the questionYour best trendTo whom the greeting card is sent?The best answer to complete dialogue above isU leanYee loan sinBloleandoYes I'm not sureWriterClack and theD Parents20 Could i have a piece of paperhere it isDO course21. Which empression shows asking suggestionABBY'S ZTH BIRTHDAY PARTY!Allegor a headacheWhat could doYou shouldDI must take a restWhat do you think about the filmNetloan't hear youYou forget itI am hungry mompleaseThe text above is written toNatha Are The delicious meals are ready on the table for you dode to congratulate someone on his birthday partyB to invite someone to attend a partyC to welcome Abby at homeA Can you give me a drink Will you have to eatD to celebrate Abby's graduationB Could you give me come meals D Do you want to exPLEASE24 Mrs Rosé Do you mind passing me the syar?Here isGRADUATIONPARTYAlolanCI'm not sureD Ya I knowCamilla CageNandoa glass of cotteEarly Yes, please. That's very kind of youA Could you heb meC Would you likeB Can you make D. Shall I have"Our mother's birthday is next weekFrom the text, we can conclude thatA The party will be held in the restaurantB. You can contact by phone to give confirmationC. All of students of class 2017 will come to theD. Dinner will not be available in the partyElin That's a good ideaWho was the bem? C Mow about giving her a presene?How old is she D. How is your motherWhat do you think about the new students inour classShe is friendly and smartAl see thatC Dont say thatB I want to sayD I thinkHappy wedding! You already said the vow, your lovehas been tied. Get ready to sail a new life I wish you allthe best I cannot wait to see little Jack and Jill soon​

Jawaban:

I am gak mudeng

Penjelasan:

It ist the puyeng

Scool ke bawah

Nurut amat sih jadi orang

7. Danival, demeru Siret MayaSementare dengan MayenBanyak May 2009. Senere street,Let walay sessiwanaCamelie my sister talainenAntarwill invite y sin tas3 The weed statement for the picture is ina The students english lesson studied in the library yesterdayBeth lesson the students studied vastarday in the libraryo the studentasudest in the hay englik yatanday lasonThe students studied analishlason in the Library yesterdaya new my father champion watching football25. I and my family are going to the to see "Laskar Pelangia Bankbu malld. post othee26. Dewi Borrow your pencil, please?Anal here you area. What can! b. May!Give me29. Father will attend a business meeting in Bandung. He goes there by place. 50, he mustava thee Harborb. airportMall28. Ben is riding his motorbike, but it almost runs out of was. So, he must go to thea bus station b. museums masque4gas station20. Ant Why da many tourist spend their holiday in BatuIta Because the scenery is veryAb. beautifuld. hot​

Jawaban:

hot 18 okee++++---&!!!

8. 16. Rafa : What does your sister usually do in the afternoon? Seva : She takes a rest after coming home from her office. Sometimes she ... and plays games on it. A. designs a computer program B. turns on the computer C. operates the machine D. takes a nap 17. Maria : Mom, finally I won the music contest. Mother : ... A. You must be better next time B. Keep on spirit C. Good luck D. I’m proud of you. 18. A : I really want to go to Lombok. B : You must go there someday. .... A. Lombok is the best place B. I want to go with you C. Lombok is not good D. You should not go there. 19. Rani : Where are you going for your holiday, Sin? Sinta : I haven't decided it yet, but ... I do really want to visit the Pisa tower (A) I must finish my term report (B) I should accompany my mom to the dentist (C) I might go to Italy with my family (D) I will just stay at home 20. Yola : Any interesting news in the newspaper ? Laily : There’s one shocking news. Yola : What’s it? Laily : one of Indonesia’s migrant workers..... in Saudia Arabia yerterday after the court found Her guilty of having murdered her employer’s wife. Yola : Oh, I am sorry to hear that A. Was executed B. Must be executed C. Will be executed D. Is executed

Jawaban:

16. Turns on computer (B)

17. I'm proud of you (D)

18. Lombok is the best place (A)

19. I might go to Italy with my family (C)

20. Was executed (A)

semoga membantu. maaf kalo salah.

9. , 19. What day Mr. Lanjar does not teach?a. Saturday and Sunday.b. Monday and Friday.c. Tuesday and Saturdayd. Friday and Saturday.20. What does Mr. Sena commonly do on Sundaymorning?a. take a travellingb. reading a newspaper.c. listening to the musicd. take a jogging.21.) Which of the following statements is NOTtrue according to the text?a. Mr. Sena doesn't teach on Thursday. b. Mr. Sena always gets up at about seven. c. o'clock in the morning.Mr. Sena's breakfast is usually an egg and toast, or oatmeal.d. Mr. Sena commonly teache sin the morning. mohon bantuannya, atas waktu nya trmks​

Jawaban:

1.A.Saturday and Sunday

2.B.Reading a newspaper

3.A.Mr.Sena doesn't teach on Thursday