# Thread: Volume of a different solid - ie next question

1. ## Volume of a different solid - ie next question

Hi again

I have another trig function so not sure what I am doing

using the V= (definite integral "S" a b) 2pi x f(x) dx formula

V = 2pi S a = 0; b=pi^1/2 sin (x^2) dx

then I am not sure what sin (x^2) dx becomes - is it = -(1/3)cos(x^3)???

I feel very confused

Thanks

Calculus beginner

2. Originally Posted by calcbeg
Hi again

I have another trig function so not sure what I am doing

using the V= (definite integral "S" a b) 2pi x f(x) dx formula

V = 2pi S a = 0; b=pi^1/2 sin (x^2) dx

then I am not sure what sin (x^2) dx becomes - is it = -(1/3)cos(x^3)???

I feel very confused

Thanks

Calculus beginner
No. Here you'll need the trig identity

$
\sin^2x = \frac{1- \cos 2x}{2}
$

3. ## next step

So is sin (x^2) = (1- cos 2x)/2 the integral or do I still need to do that?

Is (1-cos 2x)/2 the antiderivative of sin x^2??

Thanks

Calculus beginner

4. Originally Posted by calcbeg
So is sin (x^2) = (1- cos 2x)/2 the integral or do I still need to do that?

Is (1-cos 2x)/2 the antiderivative of sin x^2??

Thanks

Calculus beginner
No - it's an identity. You might recognize the following double angle formulas

$
\begin{array}{ll}
\cos 2x &= \cos^2 x - \sin^2x\\
&= 2 \cos^2x - 1\\
&= 1 - 2 \sin^2x\\
\end{array}
$