MATH 3B

Midterm 1 - Practice | General | Albrecht

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

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(b)

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(c)

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(d)

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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)

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(b)

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

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

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4. Evaluate the following. (6 points)
(a)

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(b)

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

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(b)

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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 $π/2$

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

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7.Evaluate the following integrals by any technique. Be sure to show your work or give an
explanation. (10 points)
(a)

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(b)

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