Question

Calc Problem: Help please!
Find the volume of the solid obtained by rotating the region bounded by y=9 x^2, x = 1, and y = 0, about the x-axis.

Answer 1

@campbell_st

Answer 2

ok the the formula for rotating about the x axis is

\[V = \pi \int\limits_{a}^{b} y^2 dx\]

so the values of a and b are

and then y = 0 the corresponding value of x is x = 0... so that means

a = 0 and b = 1

the graph looks like



so you are looking at

\[V = \pi \int\limits_{0}^{1} (9x^2)^2 dx\]

so just simply the (9x^2)^2

then integrate

and evaluate between x = 1 and x = 0