Find the area of the region bounded by the curves y=sinx, y=cosx, x=0 and x=pi/2

I know that they intersect at pi/4 but its kind of hard to do the area after pi/4. The integral from 0 to pi/4 would be cosx-sinx but what about the area after pi/4?

Question

Find the area of the region bounded by the curves y=sinx, y=cosx, x=0 and x=pi/2

I know that they intersect at pi/4 but its kind of hard to do the area after pi/4. The integral from 0 to pi/4 would be cosx-sinx but what about the area after pi/4?

noelgreco · Answer

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You're really looking for the area between the curves and the x-axis, so just integrate sin x from 0 to pi/4, and then cos x from pi/4 to pi/2.

anonymous · Answer

Ya just figured it out, i mixed it up with volume and thought the second part would be hard! :P