1. Evaluate the following definite or indefinite
integrals. You do not need to show work for these
problems. (10 points)
(a)

2. Set up the limit of Riemann sums you would take
to evaluate the following definite integrals. Do not
evaluate the limit. (10 points)

(a)

(a)

(c) What important theorems allows us to take
antiderivates instead of having to evaluate these
terrible limits?

3. Rewrite the following limit as a definite
integral. (3 points)

4. Evaluate the following. (6 points)

(a)

(a)

5. Evaluate the following definite and indefinite
integrals. (8 points)

(a)

(a)

6. Set up the definite integral you would take to
find each of the following volumes or areas. Do not
evaluate. (12 points)

(a) The area of the shaded region, between the first intersection of $sinx$ and $cosx$ and $π/2$

(a) The area of the shaded region, between the first intersection of $sinx$ and $cosx$ and $π/2$

(b) The object obtained by rotating the region
bounded by $y = \sqrt{x}$ and $y= \frac{1}{2}x$ about
the line $x = -2$.

7.Evaluate the following integrals by any technique.
Be sure to show your work or give an

explanation. (10 points)

(a)

explanation. (10 points)

(a)

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