Question

if f(x)=8-x^2 for -2<=x<=2, 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!

Answer 1

Just evaluate it.:
for -1 to 2, us 8-x^2, and for 2 to 3 use x^2:
\[\int\limits_{-1}^2 (8-x^2)dx+\int\limits_2^3 x^2 dx\]
Happy integrating!