Question

if f(x)=8-x^2 for -2<=x<=2 and f(x)=x^2 elsewhere, then the integral from (-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 show steps!

Answer 1

its best to draw out the piecewise function

Answer 2

i think is how it looks

Answer 3

-1 to 3 has part of this thing in the 8-x^2 and part in the x^2

Answer 4

so integrate it in parts:

\[\large \int_{-1}^{2}(8-x^2)dx+\int_{2}^{3}x^2dx\]

Answer 5

a keener eye might notice a short cut, but this method cant fail that I see

Answer 6

so is the answer d?