Question

find the area of the region in the first quadrant enclased by the X-arcis the line y=x the circle x2 + y2 =32

Answer 1

Step-by-step explanation:

r=32−−√=42–√

y=r=42–√

2y2=32

y2=16

y=4

area=∫4032−x2−−−−−−√−xdx

=∫40(4R)2−x2−−−−−−−−−√dx−∫40xdx

=(4π−8)−[x22]40

=4π−8−[16−02]

=4π−8−8

=4π−16.