I am new here, so please forgive any math formatting that is not up to spec.
I have the following problem that I need help with: "Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis.
$y=x^2, y=0, x=0, x=3$
There are 4 answers on this problem:
- $(81\div4)*\pi$
- $9\pi$
- $(243\div4)*\pi$
- $(243\div5)*\pi$
I know that to find the volume, we need to integrate these x/y values.
$$\int_0^3 \pi x(x^2-0)dx $$
Then we take the anti-derivative:
$$ \pi x^4\div4$$
Then we calculate this over the integral by substitution: $$ \pi(3)^4\div4-\pi(0)^4\div4$$
So this brings us to the answer for the area in terms of $\pi$: $(81\div4)\pi$