How do you find the volume of the bounded region if y = sinx, y = 0 from x = pi/4, x = 3pi/4, revolved around the y-axis?

1 Answer
Jun 19, 2015

Use the shell method.

Explanation:

Representative shell has volume: 2pi r h * "thickness"

r = x, h = sinx and "thickness" = dx

So the volume of the solid is given by:

V = int_(pi/4)^((3pi)/4) 2pi x sinx dx

Use integration by parts to get:

V =2pi( sinx-xcosx)]_(pi/4)^((3pi)/4

Then use trigonometry and arithmetic to get:

V =2pi* (pi sqrt2)/2 = pi^2 sqrt2