Find the volume of solid generated if the area bounded by each of the following curves is revolved about the indicated axis/line.

Question

y = x¹ + 1 , the axis, x = 3 ; OX

Answer 1

Hi Darren,

The question does appear tricky, but recall the formula for one revolution of a circle: 2πr.

Now imagine you took each revolution and added it up: 2π(summation of radii)

In other words, 2π∫₀⁴(x+1)dx is a revolution around the x-axis

and 2π∫₀³(y-1)dy a revolution around the y-axis. Once you evaluate the integrals, you should have your solutions.