Consider the function defined on the interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the function f(x)=sin⁡xf(x)=\sin x defined on the interval [0,π][0,\pi]. (i) Find the average value of ff on [0,π][0,\pi]. (ii) Define g(x)=3sin⁡(2x−π2)+4g(x)=3\sin(2x-\tfrac{\pi}{2})+4. Determine the average value of gg on the interval [π4, 3π4]\bigl[\tfrac{\pi}{4},\,\tfrac{3\pi}{4}\bigr].

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