Arti dari kata Integralialah sebuah operasi kalkulus yang bersifat antiturunan & kebalikan dari operasi turunan/peng-diferensialan
b. Penemu integral
Integral ditemukan oleh SirGriottWilhelmLebiniz pada Abad ke - 18 bersama dengan SirIsaacNewton untuk menyelesaikan permasalahan matematika yang cukup rumit
Hasil dari
adalah ![\boxed{\frac{5}{2} {x}^{2} \: + \: 2 {x}^{2} \: + C} \boxed{\frac{5}{2} {x}^{2} \: + \: 2 {x}^{2} \: + C}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cfrac%7B5%7D%7B2%7D%20%20%7Bx%7D%5E%7B2%7D%20%20%20%5C%3A%20%20%2B%20%20%5C%3A%202%20%7Bx%7D%5E%7B2%7D%20%20%5C%3A%20%20%2B%20C%7D)
PENDAHULUAN
a. Pengertian integral
Arti dari kata Integral ialah sebuah operasi kalkulus yang bersifat antiturunan & kebalikan dari operasi turunan/peng-diferensialan
b. Penemu integral
Integral ditemukan oleh Sir Griott Wilhelm Lebiniz pada Abad ke - 18 bersama dengan Sir Isaac Newton untuk menyelesaikan permasalahan matematika yang cukup rumit
c. Sifat sifat integral fungsi aljabar
1.![\displaystyle{\sf{\int {ax}^{n} \: dx = \dfrac{a}{n + 1}{x}^{n + 1} + C}} \displaystyle{\sf{\int {ax}^{n} \: dx = \dfrac{a}{n + 1}{x}^{n + 1} + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%7Bax%7D%5E%7Bn%7D%20%5C%3A%20dx%20%3D%20%5Cdfrac%7Ba%7D%7Bn%20%2B%201%7D%7Bx%7D%5E%7Bn%20%2B%201%7D%20%2B%20C%7D%7D)
2.![\displaystyle{\sf{\int k\: dx = kx + C}} \displaystyle{\sf{\int k\: dx = kx + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20k%5C%3A%20dx%20%3D%20kx%20%2B%20C%7D%7D)
3.![\displaystyle{\sf{\int \dfrac{1}{x} \: dx = ln \: x + C}} \displaystyle{\sf{\int \dfrac{1}{x} \: dx = ln \: x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%5Cdfrac%7B1%7D%7Bx%7D%20%5C%3A%20dx%20%3D%20ln%20%5C%3A%20x%20%2B%20C%7D%7D)
4.![\displaystyle{\sf{\int f(x) \pm g(x)\: dx = \int f(x) \: dx \pm \int g(x) \: dx}} \displaystyle{\sf{\int f(x) \pm g(x)\: dx = \int f(x) \: dx \pm \int g(x) \: dx}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20f%28x%29%20%5Cpm%20g%28x%29%5C%3A%20dx%20%3D%20%5Cint%20f%28x%29%20%5C%3A%20dx%20%5Cpm%20%5Cint%20g%28x%29%20%5C%3A%20dx%7D%7D)
d. Sifat sifat integral trigonometri
5.![\displaystyle{\sf{\int sin \: x\: dx = - cos \: x + C}} \displaystyle{\sf{\int sin \: x\: dx = - cos \: x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20sin%20%5C%3A%20x%5C%3A%20dx%20%3D%20-%20cos%20%5C%3A%20x%20%2B%20C%7D%7D)
6.![\displaystyle{\sf{\int sin \: (ax + b)\: dx = - \dfrac{1}{a}cos \: (ax + b) + C}} \displaystyle{\sf{\int sin \: (ax + b)\: dx = - \dfrac{1}{a}cos \: (ax + b) + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20sin%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20-%20%5Cdfrac%7B1%7D%7Ba%7Dcos%20%5C%3A%20%28ax%20%2B%20b%29%20%2B%20C%7D%7D)
7.![\displaystyle{\sf{\int k \: sin \: (ax + b)\: dx = - \dfrac{k}{a} \: sin \: (ax + b) + C}} \displaystyle{\sf{\int k \: sin \: (ax + b)\: dx = - \dfrac{k}{a} \: sin \: (ax + b) + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20k%20%5C%3A%20sin%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20-%20%5Cdfrac%7Bk%7D%7Ba%7D%20%5C%3A%20sin%20%5C%3A%20%28ax%20%2B%20b%29%20%2B%20C%7D%7D)
8.![\displaystyle{\sf{\int cos \: x\: dx = sin \: x + C}} \displaystyle{\sf{\int cos \: x\: dx = sin \: x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20cos%20%5C%3A%20x%5C%3A%20dx%20%3D%20sin%20%5C%3A%20x%20%2B%20C%7D%7D)
9.![\displaystyle{\sf{\int cos \: (ax + b)\: dx = \dfrac{1}{a} \: sin \: (ax + b) + C}} \displaystyle{\sf{\int cos \: (ax + b)\: dx = \dfrac{1}{a} \: sin \: (ax + b) + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20cos%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20%5Cdfrac%7B1%7D%7Ba%7D%20%5C%3A%20sin%20%5C%3A%20%28ax%20%2B%20b%29%20%2B%20C%7D%7D)
10.![\displaystyle{\sf{\int k \: cos \: (ax + b)\: dx = \dfrac{k}{a} \: sin \: (ax + b) + C}} \displaystyle{\sf{\int k \: cos \: (ax + b)\: dx = \dfrac{k}{a} \: sin \: (ax + b) + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20k%20%5C%3A%20cos%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20%5Cdfrac%7Bk%7D%7Ba%7D%20%5C%3A%20sin%20%5C%3A%20%28ax%20%2B%20b%29%20%2B%20C%7D%7D)
11.![\displaystyle{\sf{\int tan \: x\: dx = - ln |cos \: x| + C}} \displaystyle{\sf{\int tan \: x\: dx = - ln |cos \: x| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20tan%20%5C%3A%20x%5C%3A%20dx%20%3D%20-%20ln%20%7Ccos%20%5C%3A%20x%7C%20%2B%20C%7D%7D)
12.![\displaystyle{\sf{\int tan \: (ax + b)\: dx = - \dfrac{1}{a} \: ln \: |cos \: (ax + b)| + C}} \displaystyle{\sf{\int tan \: (ax + b)\: dx = - \dfrac{1}{a} \: ln \: |cos \: (ax + b)| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20tan%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20-%20%5Cdfrac%7B1%7D%7Ba%7D%20%5C%3A%20ln%20%5C%3A%20%7Ccos%20%5C%3A%20%28ax%20%2B%20b%29%7C%20%2B%20C%7D%7D)
13.![\displaystyle{\sf{\int tan \: (ax + b)\: dx = - \dfrac{k}{a} \: ln \: |cos \: (ax + b)| + C}} \displaystyle{\sf{\int tan \: (ax + b)\: dx = - \dfrac{k}{a} \: ln \: |cos \: (ax + b)| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20tan%20%5C%3A%20%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20-%20%5Cdfrac%7Bk%7D%7Ba%7D%20%5C%3A%20ln%20%5C%3A%20%7Ccos%20%5C%3A%20%28ax%20%2B%20b%29%7C%20%2B%20C%7D%7D)
14.![\displaystyle{\sf{\int cot \: x\: dx = ln |sin \: x| + C}} \displaystyle{\sf{\int cot \: x\: dx = ln |sin \: x| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20cot%20%5C%3A%20x%5C%3A%20dx%20%3D%20ln%20%7Csin%20%5C%3A%20x%7C%20%2B%20C%7D%7D)
15.![\displaystyle{\sf{\int cot \:(ax + b)\: dx = \dfrac{1}{a} ln|sin \:(ax + b)| + C}} \displaystyle{\sf{\int cot \:(ax + b)\: dx = \dfrac{1}{a} ln|sin \:(ax + b)| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20cot%20%5C%3A%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20%5Cdfrac%7B1%7D%7Ba%7D%20ln%7Csin%20%5C%3A%28ax%20%2B%20b%29%7C%20%2B%20C%7D%7D)
16.![\displaystyle{\sf{\int k \: cot \:(ax + b)\: dx = \dfrac{k}{a} ln|sin \:(ax + b)| + C}} \displaystyle{\sf{\int k \: cot \:(ax + b)\: dx = \dfrac{k}{a} ln|sin \:(ax + b)| + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20k%20%5C%3A%20cot%20%5C%3A%28ax%20%2B%20b%29%5C%3A%20dx%20%3D%20%5Cdfrac%7Bk%7D%7Ba%7D%20ln%7Csin%20%5C%3A%28ax%20%2B%20b%29%7C%20%2B%20C%7D%7D)
17.![\displaystyle{\sf{\int {sec}^{2}x \: dx = tan \: x + C}} \displaystyle{\sf{\int {sec}^{2}x \: dx = tan \: x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%7Bsec%7D%5E%7B2%7Dx%20%5C%3A%20dx%20%3D%20tan%20%5C%3A%20x%20%2B%20C%7D%7D)
18.![\displaystyle{\sf{\int {csc}^{2}x \: dx = - cot \: x + C}} \displaystyle{\sf{\int {csc}^{2}x \: dx = - cot \: x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%7Bcsc%7D%5E%7B2%7Dx%20%5C%3A%20dx%20%3D%20-%20cot%20%5C%3A%20x%20%2B%20C%7D%7D)
19.![\displaystyle{\sf{\int {sin}^{n}x. \: cos \: x \: dx = \dfrac{1}{n + 1}{sin}^{n + 1}x + C}} \displaystyle{\sf{\int {sin}^{n}x. \: cos \: x \: dx = \dfrac{1}{n + 1}{sin}^{n + 1}x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%7Bsin%7D%5E%7Bn%7Dx.%20%5C%3A%20cos%20%5C%3A%20x%20%5C%3A%20dx%20%3D%20%5Cdfrac%7B1%7D%7Bn%20%2B%201%7D%7Bsin%7D%5E%7Bn%20%2B%201%7Dx%20%2B%20C%7D%7D)
20.![\displaystyle{\sf{\int {cos}^{n}x. \: sin \: x \: dx = - \dfrac{1}{n + 1}{cos}^{n + 1}x + C}} \displaystyle{\sf{\int {cos}^{n}x. \: sin \: x \: dx = - \dfrac{1}{n + 1}{cos}^{n + 1}x + C}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Csf%7B%5Cint%20%7Bcos%7D%5E%7Bn%7Dx.%20%5C%3A%20sin%20%5C%3A%20x%20%5C%3A%20dx%20%3D%20-%20%5Cdfrac%7B1%7D%7Bn%20%2B%201%7D%7Bcos%7D%5E%7Bn%20%2B%201%7Dx%20%2B%20C%7D%7D)
PENYELESAIAN
● DIKETAHUI
● DITANYA
hasil integral dari : 5x + 4x dx
● DIJAWAB
PELAJARI LEBIH LANJUT
brainly.co.id/tugas/16006687
brainly.co.id/tugas/15612833
brainly.co.id/tugas/28839928
DETAIL JAWABAN
Mata pelajaran : Matematika
Kelas : 11
Jenjang : Sekolah Menengah Atas
BAB : 10 - Integral Fungsi Aljabar
SubBAB : Integral Tak Tentu
Materi : Menghitung Integral Tak Tentu
Kode soal : 2
Kode kategorisasi : 11.2.10
Kata kunci : Integral