I am attempting to solve the following problem and would like some validation in my approach/need some help on finding zeros if this is indeed the correct approach.
Find vol of solid of revolution - The region bounded by $y = x−4x^2$ and the $x$-axis revolved about the $y$-axis.
- $V= 2\pi$ * [integral of $\int_a^b x(x-4x^2)dx$
- evaluate from b to a, and I'm assuming answer would be in pi cubic units because we're solving for volume.
How would I determine the bounds, and is my approach the correct one? (apologies for the poor formatting, I am new to the site)