Question

Can anyone help me with this. find the following antiderivative of ∫(sin^4 x) (cos^3 x) dx.

Answer 1

sin^2 x + cos ^2 x = 1

Answer 2

lop of one of the sin factors, then use the half angle forumals.

Answer 3

can I let u=cos x, if I want to use substitution ?

Answer 4

after using the half angle forumals, you can let sin x equal u

Answer 5

yea, use u = sin, integrand becomes (u^4 )(cos^2 x) = u^4( 1- u^2 ) = u^4-u^6 du

Answer 6

ok. I got the idea. means I have to change cos^2 x = 1- sin^2 x right ?
can I do this ?
(sin^4 x) ( cos^3 x )=(sin^4 x ) (1- sin^2 x ) cos x dx
then I let u= sin x. I'll get u^2 (1- u^2 ) du. is it right ?

Answer 7

right with the sub u=sin x then you lose one of the cos x fomr the integrans leaving a cos^2 x which equals, because of the sub ( 1 - u^2)

Answer 8

so the integral becomes u^4 ( 1 - u ^ 2 ) = u^4 - u^6
I put it in a symbolic integrator and go a different answer but numerically it works.

Answer 9

ok. I got it. thanks a lot, roachie.

Answer 10

yup