Posted by **ronnieday** on Friday, March 23, 2012 at 12:13pm.

Let R be the region bounded by the y-axis and the curves y = sin x and y = cos x. Answer the following.

a)Find the exact area of R.

b)A solid is generated by revolving R about the x-axis. Find the exact volume of the solid.

- Calculus -
**Steve**, Friday, March 23, 2012 at 12:28pm
The curves intersect at (pi/4,1/√2)

On that interval, cos(x) > sin(x), so

A = ∫[0,pi/4](cosx-sinx)dx

= sinx+cosx[0,pi/4]

= (1/√2+1/√2)-(0+1) = √2-1

V = ∫[0,pi/4]pi*(R^2-r^2)dx

where R=cosx and r=sinx

V = pi*∫[0,pi/4](cos^2-sin^2)dx

= pi*∫[0,pi/4]cos(2x) dx

= pi/2 sin(2x)[0,pi/4]

= pi/2 * (1-0)

= pi/2

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