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
