[Steps Shown] Consider the function f(t)=(4-t) e^-t / 2 Find F(x)=∫_0^π f(t) d t without the aid of a computer/calculator. Verify your answer by
Question: Consider the function \(f(t)=(4-t) e^{-t / 2}\)
- Find \(F(x)=\int_{0}^{\pi} f(t) d t\) without the aid of a computer/calculator. Verify your answer by differentiation.
- Graph \(f(t)\) and \(F(x)\)
- Give a geometric interpretation of \(F(x)\) for a particular value of \(x\) on the interval [0,4]. Identify your answer by shading the region on the graph in part \(\mathrm{b}\).
Deliverable: Word Document 
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