- #1

- 559

- 8

## Homework Statement

Find the volume of the solid obtained by rotating the region

bounded by the given curves about the specified line. Sketch the

region, the solid, and a typical disk or washer.

y=sinx, y=cosx, 0≤ x≤∏/4, About y=-1

## Homework Equations

## The Attempt at a Solution

Tried 2 ways, shell method and washer method..

[tex]\pi \int_0^\frac{\pi}{4}(cosx-sinx)^{2}\,dx - \pi \int_0^\frac{\pi}{4}(-1)^{2}\,dx[/tex]

[tex]\pi \int_0^\frac{\pi}{4}cos^{2}x-2sinxcosx+sin^{2}x\,dx - \pi \int_0^\frac{\pi}{4}1\,dx[/tex]

^Hard integral

[tex]2\pi \int_0^\frac{\pi}{4}(x+1)(cosx-sinx)\,dx[/tex]

[tex]2\pi \int_0^\frac{\pi}{4}xcosx+cosx-xsinx-sinx\,dx[/tex]

[tex]2\pi (sinx+cosx)|[/tex] (From 0 to ∏/4, not sure how to do this in latex)

(And so on)

Thanks for any help.

Last edited: