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) ]

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