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1. Use geometry to evaluate the following integral \(\int_{-2}^3 \mid x \mid dx\). It will really help if you draw the curve.

a.  \(\frac{15}{2}\)

b.  \(\frac{13}{2}\)

c.  \(\frac{9}{2}\)

d.  \(\frac{1}{2}\)

e.  \(\frac{-1}{2}\)

2. Which one of the following represents a right hand sum for the function \(f(x) = 2^x\) between \(x = 0\) and \(x = 2\) with \(n = 4\) equal subintervals.

a.  \((\frac{1}{2})(\sqrt{2}) + (\frac{1}{2})(2) + (\frac{1}{2})(2\sqrt{2}) + (\frac{1}{2})(4)\)

b.  \((\frac{1}{4})(\sqrt{2}) + (\frac{1}{4})(2) + (\frac{1}{4})(2\sqrt{2}) + (\frac{1}{4})(4)\)

c.  \((\frac{1}{4})(\sqrt{2}) + (\frac{1}{2})(2) + (\frac{3}{4})(2\sqrt{2}) + (1)(4)\)

d.  \((\frac{1}{2})(\sqrt{2}) + (1)(2) + (\frac{3}{2})(2\sqrt{2}) + (2)(4)\)

e.  \((\frac{1}{2})(\frac{1}{4}) + (\frac{1}{2})(1) + (\frac{1}{2})(\frac{9}{4}) + (\frac{1}{2})(4)\)

3. Consider the area under the curve \(y = f(x) = 1 - x^2\) between \(x = 0\) and \(x = 1\). (It will help you answer this question if you draw the curve first.)

a.  The left-hand-sum with \(n=4\) subintervals is an underestimate of the true area under the curve.

b.  The right-hand-sum with \(n=4\) subintervals is an underestimate of the true area under the curve.

c.  The right-hand-sum with \(n=4\) subintervals is an overestimate of the true area under the curve.

d.  None of the above are true.