Lt f be a continuous function on the interval 0 2 which

Question

Let f be a continuous function on the interval [0, 2] which satisfies∫20f(x) dx = 5. Given this information, compute the integral ∫10f(2y) dy.Show your work and justify your answer. Solution: Use the substitution x = 2y, dx = 2 dy, dy =12dx, x(0) =2(0) = 0, x(1) = 2(1) = 2 to find∫10f(2y) dy = ∫20f(x)12dx =12 ∫20f(x) dx =12(5) =52.