true or false?

Question

if f(x) is an even function,

(above integral sign: 0  below integral sign: -a) ∫f(x)dx= (above integral sign: a  below integral sign: 0) -∫f(x)dx

 

true or false?

Answer 1

Let f(x) = cosx even function Then ∫_-π/2⁰cosxdx = sinx_-π/2⁰ = sin0 - sin(- π/2) = 1

-∫₀^π/2cosxdx = - inx₀^π/2 = - 1. This contrexample shaw that statement not right