10 points consider the integral f x dx where f x page

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Unformatted text preview: First Exam — January 28, 2010 1 3. (10 points) Consider the integral f (x) dx, where f (x) = √ Page 6 of 11 1 + x3 . 0 (a) Estimate the error made in approximating the value of this integral using the Trapezoidal Rule with n = 10 subintervals. State your answer in a complete sentence. You may make use of the 3x(x3 + 4) fact that f (x) = . 4(x3 + 1)3/2 (b) Would the Trapezoidal Rule approximation described in part (a) give an overestimate or underestimate of the actual value, or is it impossible to tell with the information given? Explain briefly. (c) Again using the Trapezoidal Rule, how many subintervals n would be necessary to guarantee an error of at most 10−6 ? Give a valid n in simplified form. (As long as you justify your answer, you do not have to worry about finding the best possible value.) Math 42, Winter 2010 First Exam — January 28, 2010 Page 7 of 11 4. (8 points) (a) Set up, but do not evaluate, an integral representing the area of the region bounded by the curves y = 5 − x2 and y = x2 + 3x + 3. As justification, draw a picture with a sample slice labeled. (b) Set up an integral representing the volume obtained by rotating the region from part (a) about the x-axis. Make sure you justify your answer (draw and label a diagram). Again, don...
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This note was uploaded on 07/31/2013 for the course MATH 42 taught by Professor Butscher,a during the Spring '07 term at Stanford.

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