- #1
iRaid
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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.
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