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# Test4A - pts Express Z 5 2 sin x dx as a limit of Riemann...

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MA141-001 Test 4A April 23, 2010 Amanda Smith North Carolina State University Department of Mathematics Please put all work in the stamped blue book that has been provided. Nothing on this test sheet will be graded. Please put one problem on each page; you are allowed to use the back of the sheet as a new page. No calculators, formula sheets, or other aids are permitted. Please show all of your work. Simplify all solutions completely and clearly indicate your answers. Write your name on both the blue book and this test sheet. 1. [10 pts. ] If f ( x ) = x 2 + 1, then estimate the area under the curve from 0 to 4 by using four evenly-spaced rectangles and by taking the sample points to be the right endpoints. 2. [6
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Unformatted text preview: pts. ] Express Z 5 2 sin ( x ) dx as a limit of Riemann sums. (Do not evaluate.) 3. [12 pts. ] Evaluate Z 1 (5 + 4 x 3 ) dx . 4. [8 pts. ] Evaluate each of the following: (a) Z a x dx (b) Z sec 2 ( x ) dx (c) Z 1 x 2 + 1 dx (d) Z 1 x dx 5. [6 pts. ] Find the derivative of the function g ( y ) = Z y 2 t 3 cos ( t ) dt . 6. [12 pts. ] Evaluate Z 2 x 2 p x 3 + 1 dx . 7. [12 pts. ] Evaluate Z sin ( ln ( x )) x dx . 8. [12 pts. ] Evaluate Z te t dt . 9. [12 pts. ] Evaluate Z cos 3 ( x ) dx . 10. [10 pts. ] Evaluate Z 2 p 4-x 2 dx by the trigonometric substitution. Bonus : [2 pts. ] Explain the diﬀerence between Z t 2 t 1 v ( t ) dt and Z t 2 t 1 | v ( t ) | dt ....
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