Consider the given function and the given interval. f(x) = 8 sin(x) ? 4 sin(2x), [0, ?] (a) Find the average value fave of f on the given interval. fave = 16/? (b) Find c such that fave = f(c). (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Added by Lourdes C.
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Let's denote # as b for simplicity. So we need to calculate: fave = (1/b) ∫ from 0 to b (8sin(x) - 4sin(2x)) dx The integral of sin(x) is -cos(x) and the integral of sin(2x) is -1/2 cos(2x). So we have: fave = (1/b) [ -8cos(x) + 2cos(2x) ] from 0 to Show more…
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