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samw08m2 - y-axis and y = 2-x bound a region Calculate the...

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MAT 21B Sample Problems for Midterm II 1) (True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a: i π 2 π 4 cot ( t ) dt = 1 2 ln 2 b: The center of mass is a force on a thin plate. c: ( x + y ) 2 = x 2 + y 2 d: A theorem of Pappus relates the volume of a rotational solid to the center of mass of the region revolved about an axis to create the solid. e: The circumference of a circle of radius 5 is 10 π . 2) (8 points) Find the area bounded by the curves y = cosz 4+3 sinz dz, the x -axis, x = - π 2 and x = π 2 . 3) (12 points) The x -axis, the
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Unformatted text preview: y-axis and y = 2-x bound a region. Calculate the volume of the solid of revolution obtained by rotating this region about the x-axis in two di±erent ways: (a) the washer method; (b) the cylindrical shells method. 4) (8 Points) Find the length of the curve parametrized by x = cost , y = t + sint , 0 ≤ t ≤ π . 5) (12 points) (Center of mass or surfaces of revolution) Find the area of the surface of revolution obtained by rotating the arc y = √ x , 3 / 4 ≤ x ≤ 15 / 4 about the x-axis. 1...
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