Consider the given function and the given interval.

Question

f(x) = 10 sin(x) − 5 sin(2x), [0, π]
(a) Find the average value fave of f on the given interval.
(b) Find c such that fave = f(c). (Round your answers to three decimal places.)

Answer 1

(a) [∫[0,π] (10 sin(x)-5sin(2x)) dx]/(π-0) = 20/π

(b) 10sin(c)-5sin(2c) = 20/π
c ≈ 1.238 or 2.808