Question

if f(x)=8-x^2 for -2<=x<=2 and f(x)=x^2 elsewhere, then the integral [-1, 3] f(x)dx is a number between..
a. 0 and 8
b. 8 and 16
c. 16 and 24
d. 24 and 32
e. 32 and 40
please help and show steps!

Answer 1

int[-1,3](f(x)dx) = int[-1,2](8-x^2)dx + int[2,3](x^2)dx => 8x-x^3/3|[-1,2] + x^3/3[2,3]
8(2)-2^3/3 - [8(-1) - (-1)^3/3] + 3^3/3 - 2^3/3 => 16-8/3 + 8 - 1/3 + 9 - 8/3