EXAMPLE 5 Find the area of the region bounded by the curves y = sin(x), y = cos(x), x = 0, and x = 7/2. SOLUTION The points of intersection occur when sin(x) = cos(x), that is, when x = (since 0sxs n/2). The region is sketched in the figure. Observe that cos(x) > sin(x) when , but sin(x) 2 cos(x) when Therefore the required area is 피2 ! Icos(x) – sin(x)| dx = A1 + A2 A = 7/4 /2 | (cos(x) – sin(x)) dx + 7/4 (sin(x) – cos(x)) dx 7/4 7/2 + 피/4 -0 - 1 + -0 - 1 + = 2/2 - 2. In this particular example we could have saved some work by noticing that the region is symmetric about x = n/4 and so /4 A = 2A, = 2 (cos(x) – sin(x)) dx. Jo

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