Exam 3 Solutions

Exam 3 Solutions - Calculus I Exam 3 Review 4.3-5.6 skip...

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Calculus I Exam 3 Review, 4.3-5.6 skip 4.7 and 5.5 You may not use any programs to evaluate Riemann sums, integrals, areas, or volumes. Work must be shown for these. 1. Find the derivative of the function () cos 2 3 1 1 x gx td t =− . 2. Evaluate the integral if it exists. a. 2 32 1 83 x xd x + b. 1 0 sin 3 t π c. 2 2 4 x dx x x + + d. 2 23 0 1 yy d y + e. 5 2 1 4 dt t f. 53 dx x
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g. cos sin t et d t 3. Find the volume of the solid obtained by rotating the region bounded by 2 y x = and 2 yx = about the x-axis. 4. Find the volume of the solid obtained by rotating the region bounded by 2 1 x y =+ and 3 =− about the y-axis. 5. Find the volume of the solid obtained by rotating the region bounded by 3 = and 2 = about 1 y = . Set up, but do not evaluate. ( ݔ ൒ݔ ݋݊ ሾ0,1ሿ )
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6. Find the volume of the solid obtained by rotating the region bounded in the first quadrant by 3 yx = and 2 2 x =− about the y-axis. Use the method of cylindrical shells. 7. Why is the Fundamental Theorem of Calculus important? 8. Evaluate ( ) 1 2 0 1 x xd x +− by interpreting it in terms of area. 9. If () 6 0 10 fxd x = and 4 0 7 x = , find 6 4 f xdx . 10. Find the area of the region bounded by
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This note was uploaded on 04/07/2009 for the course M 408 taught by Professor Hodges during the Spring '08 term at University of Texas.

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Exam 3 Solutions - Calculus I Exam 3 Review 4.3-5.6 skip...

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