Question

int x^2/sqrt(9-x^2) please help :)

Answer 1

Seems like a trig sub.

Answer 2

i got x=3sintheta
dx=3costhetadtheta

Answer 3

so \[\int\limits_{}^{}9\sin^2\theta/\sqrt{9-9\sin^2\theta}(3\cos \theta d \theta)\]

Answer 4

now where im lost is the book says "simplify" and then makes it into \[9\int\limits_{}^{}\sin^2\theta d \theta\]

Answer 5

with no explanation of what happened to everything else and i don't know how this was simplified?

Answer 6

\[
\int \frac{9\sin^2\theta}{\sqrt{9-9\sin^2\theta}}3\cos \theta d \theta =
\int \frac{9\sin^2\theta}{\sqrt{9(1-\sin^2\theta)}}3\cos \theta d \theta = \\
\int \frac{9\sin^2\theta}{\sqrt{9\cos^2\theta)}}3\cos \theta d \theta =
\int \frac{9\sin^2\theta}{3\cos\theta}3\cos \theta d \theta = \int 9\sin^2(\theta)d\theta

\]

Answer 7

AHH ok thank you so much

Answer 8

You are welcome.

Answer 9

ok just one thing though if you have sqrt 9cos^2theta

Answer 10

Ahh he beat me to it! haha. Yeah you were on the right path :D

Answer 11

ahhh you square rooted it

Answer 12

you sly devil you

Answer 13

You can factor out the 9 and treat cos theta as a constant, therefore pulling out of one them you'll have 3 cos theta.