Question

if f is continuous and the integral [0,4] f(x)dx=10 find the integral [0,2]f(2x)dx

Answer 1

let t =2x, now

integ {0,2} f(2x)dx becomes

integ {0,4} f(t) dt/2

because when x=0, t=0 and when x=2, t=4

and dx = dt/2


hence the answer is 10/2 =5