MWF Midterm 1 (Fall 2009)

# MWF Midterm 1 (Fall 2009) - Do not evaluate the integral(b...

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MAT 296 Hour Test 1 (MWF sections) October 8, 2009 Do all the following problems. To receive full credit for an answer or to have it considered for partial credit, you must show your work . This test has 7 problems on 7 pages. Make sure your test is complete! 1. (14 points) A region is bounded by the curves y = x 2 and y = 2 x + 3. (a) Sketch the region. (b) Find the area of the region. 2. (12 points) A solid S is obtained by rotating the region bounded by y = x 2 + 4, y = 4 x , and x = 0 around the y -axis. (a) Set up an integral for ﬁnding the volume of S. Do not evaluate the integral. (b) What method did you use to part (a)? 3. (12 points) A solid is obtained by rotating the region bounded by x = 1 y , x = 0, y = 1, and y = 3 around the line x = - 1. (a) Set up an integral for ﬁnding the volume of S.
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Unformatted text preview: Do not evaluate the integral. (b) What method did you use to part (a)? 4. (12 points) A bucket full of water is hanging down a well at the end of a 30 ft rope. The bucket and water together weigh 20 lbs. The rope has a density of 0.5 lb/ft. Set up an integral for calculating how much work is done lifting the bucket to the top of the well. Do not evaluate the integral. 5. (20 points) Evaluate each of the following deﬁnite integrals: (a) Z π/ 2 sin 2 x cos xdx (b) Z π/ 4 tan 2 θ sec 4 θ dθ 6. (24 points) Find the following indeﬁnite integrals: (a) Z x 2 ln xdx (b) Z 1 √ x 2 + 4 dx (c) Z x 2 √ 16-x 2 dx 7. (6 points) Find the following indeﬁnite integral Z √ x 2 + 4 x + 5 dx...
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