Question

find the antiderivitive of sin^3(x)

Answer 1

Use the identity
\[\cos^2(x) + \sin^2(x) = 1\]

so
\[\int\limits_{}^{} \sin^3(x) dx = \int\limits_{}^{} (1-\cos^2(x)) \sin(x) dx\]
try doing that integral now

Answer 2

Cheers thanks, I'll let you know

Answer 3

your welcome

Answer 4

I'm really stumped, can you help me out some more?

Answer 5

use a u-substitution
u = 1 - cos^2(x)
du = -2cos(x)
-du/2 = cos(x)

try doing it now

Answer 6

Thanks

Answer 7

Do I change cos^2 (x) into 1/2[1+cos(2x)]?

Answer 8

actually try
u= cos x
then du = - sin x dx
and then you integral becomz
\(\large - \int (1-u^2)du\)
which is pretty easy to integrate :)

Answer 9

Thankyou :)

Answer 10

welcome ^_^
let us know if you get stuck in any step ...