consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral:

Question

(a) definite integral from 0(on the bottom of the integral sign) to 5(top of integral sign) of[f(x)+2]dx

(b) definite integral from -5(bottom of integral sign) to 5(top of integral sign) f(x)dx, given that f is an even function.

Answer 1

This was done by Damon, but here's my take

∫[0,5](f(x)+2) dx
= ∫[0,5] f(x) dx + ∫[0,5] 2 dx
= 4 + 2x[0,5]
= 4 + 10
= 14

Since we are dealing with an even function,
∫[-5,5] f(x) dx = 2∫[0,5] f(x) dx = 2*4 = 8