U substitution

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1. Feb 28, 2016

The Subject

1. The problem statement, all variables and given/known data
Im looking over the notes in my lecture and the prof wrote,
$$\int_{0}^{2} \pi(4x^2-x^4)dx=\frac{64\pi}{15}$$
Im wondering whats the indefinite integral of this equation.

2. Relevant equations
using u substitution

3. The attempt at a solution
$$\int \pi(4x^2-x^4)dx= \pi \int x^2(4-x^2)dx \\ u = 4 - x^2 \ \ \ \ \ \ \ \ \ \ -\frac {1}{2} du =xdx \\$$

Im confuse since i have an x^2 but my du=x.

I attempted to also use from u to get,
$$x=\sqrt{4-u} \\ \pi \int \frac{1}{2}u\sqrt{4-u}dx$$
but it seems this made the formula harder to integrate...or am i just giving up too quickly

2. Feb 28, 2016

Samy_A

You are making this far too complicated.

What is $\int x^n dx$, (for $n \geq 1$)?

3. Feb 28, 2016

The Subject

That makes sense...

I was working on a bunch of u sub equations earlier. I guess I was on a u sub mode

Thanks a lot!