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2010midterm2_soln

# 2010midterm2_soln - Solution to MAT21B Midterm II Spring...

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Solution to MAT21B Midterm II, Spring 2010 Problem I: Multiple Choices. (70 points total, 7 points each). Please fill in your answers in the following table : Problems #1 #2 #3 #4 #5 #6 #7 # 8 #9 10 Answers C B D B A A C D B C 1. The region bounded by the curve y = x 2 + 3 and the line y = 4 x is revolved about the x - axis to generate a solid. Find the volume of the solid. A. V = R 3 1 2 π [( x 2 + 3) - 4 x ] dx B. V = R 3 1 2 π [4 x - ( x 2 + 3)] dx C. V = R 3 1 π h 16 x 2 - ( x 2 + 3) 2 i dx D. V = R 3 1 π h ( x 2 + 3) 2 - 16 x 2 i dx . 2. The region bounded by the curve y = sin 4 x x and the x - axis between π 2 , π is revolved about the y - axis to generate a solid. Find the volume of the solid. A. V = R π π 2 π sin 8 x x 2 dx B. V = R π π 2 2 π sin 4 xdx C. V = R π π 2 2 π sin 4 x x dx D. V = R π π 2 πx sin 4 xdx 3. Find the length of the parametric curve x = cos 4 ( t ), y = sin 4 ( t ) on the interval 0 t 2 π A. L = 16 R 2 π 0 cos 6 ( t ) sin 2 ( t ) + sin 6 ( t ) cos 2 ( t ) dt B. L = R 2 π 0 ( cos 4 t + sin 4 t ) dt C. L = R 2 π 0 16 cos 6 t + 16 sin 6 tdt D. L = R 2 π 0 p 16 cos 6 ( t ) sin 2 ( t ) + 16 sin 6 ( t ) cos 2 ( t ) dt 4. Find the center of the rod with variable density

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