QUIZ #13: CALCULUS 1A (Stankova) Wednesday, April 28, 2004 Section 10:00–11:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Let g(x) = ∫_{−2}^{x} f(t) dt, where f is the function shown.

(a) Evaluate g(−2).

(b) Is g(4) > 0? Explain.

(c) Estimate g(0).

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(d) Where does g have a maximum value in the interval [−2, 4]?

(e) Draw a (very) rough graph of g.

QUIZ #13: CALCULUS 1A (Stankova) Wednesday, April 28, 2004 Section 11:00–12:00 (Voight)

Name:

Please complete the following problem(s) in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. Use the Fundamental Theorem of Calculus (Part 1) to find the derivative of the function

y = ∫_{1}^{x^{2}}(\sqrt{t} + ln t) dt.

Problem 2. Use the Fundamental Theorem of Calculus (Part 2) to evaluate the integral.

∫_{1}^{2} \frac{6 + \sqrt{u}}{u^{2}} du.