Question

Reduction formula
∫sin^7x dx

Answer 1

@ganeshie8

Answer 2

@ajprincess

Answer 3

@ajprincess

Answer 4

put cosx = t
-sinx dx = dt

Answer 5

\(\large \mathbb{\int \sin^7x dx }\)

\(\large \mathbb{\int \sin^6x ~ \sin xdx }\)

\(\large \mathbb{\int (\sin^2x)^3 ~ \sin xdx }\)

\(\large \mathbb{\int (1-\cos^2x)^3 ~ \sin xdx }\)

put cosx = t
-sinx dx = dt

\(\large \mathbb{-\int (1-t^2)^3 ~ dt}\)

Answer 6

expand the cubic and integrate each term

Answer 7

the answer is -cosx+cos^3x-3cos^5x/5+cos^7x/7+c @ganeshie8

Answer 8

right?

Answer 9

\(\large \color{red}{\checkmark}\color{red}{\checkmark}\)

Answer 10

Thank you sir :)

Answer 11

np :)

Answer 12

:)