Question

Find the area of the region bounded by the x-axis and the curves y=7sin(x) and y=7 cos(x) where x∈[0,(π/2)]

Answer 1

To calculate the area between both curves, we must calculate the following integrals:
 int a-b [f (x)] dx
 int a-b: integral from a to b
 f (x): function
 Enter [0, (π / 2)]
 int 0-π / 2 [(7 cos (x) -7sin (x))] dx = int 0 -π / 2 [(7 cos (x)] dx + int 0-π / 2 [-7sin (x) )] dx
 Calculated:
 int 0-π / 2 [(7 cos (x)] dx = 7 (sin (π / 2) - sin (0)) = 7 (1-0) = 7
 int 0-π / 2 [-7 sin (x))] dx = 7 (cos (π / 2) - cos (0)) = 7 (0-1) = - 7
 int 0-π / 2 [(7 cos (x) -7sin (x))] dx = 7 + (-7) = 0
 answer
 the area of the region bounded by the x-axis and the curves y = 7sin (x) and y = 7 cos (x) where x∈ [0, (π / 2)] is
 A=0