The Integral A 4 B 4 16 X 2 Dx Gives The Area Of A Region R In The Xy Plane

The integral a=-5, b=5, ∫√(25−x^2)dx gives the area of a region R in the xy−plane.

a) Identify and sketch the region R.

b) Find the area of R using a known geometric formula, not by evaluating the

integral.

Solution

R is the upper half of a circle centered at (0,0) with radius 4

PI*r^2 is the area of the circle. divide that by 2 (half a circle)

not sure what C means. part b is the exact value of the integral.