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MT2-Practice

# MT2-Practice - a the x-axis b the y-axis 3(10 marks a Find...

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Math 101 - Section 208 - Practice Midterm #2 Instructor: Michael Lindstrom March 8, 2010 1 (15 marks: 3 marks each part) a Find integraltext e - x 9+ e - 2 x dx. b Find the average value of y = sin( x ) on the interval [0 , π 2 ] . Hint: start with a substitution. c Plot the polar curve r = sin(3 θ ) . d Find the area lying outside the polar curve r = 1 3 cos( θ ) and inside the polar curve r = 5 . e Evaluate integraltext 3 - 3 4 16 - s 2 ds. 2 (10 marks) Find the volume of the resulting solid if the region under the curve y = 1 x 2 +3 x +2 from x = 0 to x = 1 is rotated about

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Unformatted text preview: a the x-axis b the y-axis 3 (10 marks) a Find i csc 6 θdθ. b Find i-3-4 dx ( x 2-4) 3 / 2 . 4 (10 marks) The plot of r = cos( θ/ 2) is given in ±gure 1. Find the area of the shaded region. 5 (5 marks) Give the formula/algorithm for integration by parts, for both a de±nite and inde±nite integral that admit this form of manipulation. Justify why the algorithm is correct. 1 Figure 1: Polar curve r = cos( θ/ 2) . 2...
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MT2-Practice - a the x-axis b the y-axis 3(10 marks a Find...

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