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1271practicemidterm3

# 1271practicemidterm3 - Name Signature Section Math 1271...

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Name: Signature: Section: Math 1271. Lecture 030 Practice Midterm Exam III There are a total of 100 points on this 50 minute exam. To get full credit for a problem you must show the details of your work. Answers unsupported by an argument will get little credit. No books, notes, calculators, cell phones or other elecronic devices are allowed. Do all of your calculations on this test paper. Problem Score 1. 2. 3. 4. 5. Total: 1

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Problem 1 Find the derivative f ( x ) and simplify. a. (5 points) f ( x ) = ln( e x - 2 ) b. (5 points) f ( x ) = x x 4 2
c. (5 points) f ( x ) = integraldisplay 3 x 1 + t 3 dt d. (5 points) f ( x ) = integraldisplay 5 x 2 1 1 sin( t 3 ) dt. 3

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Problem 2 Compute the integrals. Note that some of these integrals are indefinite and some definite. a. (5 points) integraldisplay π/ 2 0 cos x sin x 3 + cos 2 x dx b. (5 points) integraldisplay ( x + 1) 2 (1 - x 2 ) 2 dx 4
c. (5 points) integraldisplay 2 0 (1 + x ) 3 / 2 dx d. (5 points) integraldisplay e x ( e x + 1) 3 dx 5

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Problem 3 (20 points) Find the area of the finite region in the plane bounded by the curve y = - x 2 + x + 2 and the x -axis.
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