Find the range of the function f of x equals the integral from negative 4 to x of the square root of the quantity 16 minus t squared

Question

 

Find the range of the function  .

A)[-4,4]

B)[-4,0]

C)[0,4pi]

D)[0,8pi]

My answer is C

Answer 1

Since the integrand is the function for the top-half of the semicircle with radius 4 centered at (0,0), the max area is (4²π)/2= 8π! So that would be D!