\text { 2. Let } F(x)=\int_{0}^{x}\left[\cos \left(\frac{t}{2}\right)+\left(\frac{3}{2}\right)\right] \cdot d t \text { on the closed interval }[0,2 \pi] \text {. } a. Approximate F(2t) using four right hand rectangles. b. Find F'(2n). c. Find the average value of F'(x) on the interval [0,47].

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