Evaluate integral from negative 3 to 3 of f of x, dx for f of x equals square root of quantity 4 minus the square of the quantity x plus 1 for x is between negative 3 and...

Question

 

Use geometry to evaluate  for  . (2 points)

A	2π + 1
B	2π - 1
C	π - 1
D	π + 1

Answer 1

The integral between -3 and 1 is the area of a half of a circle of radius 2,which is 1/2π*2² = 2π

The integral between 1 and 3 is the negative of that of a triangle of height 1 (at 2) and base 2 (from 1 to 3), which is 1.

Thus, the area is 2π - 1

B