MAC 2312 Midterm: MAC2312 F97 Test 2
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October 13, 1997: r is the region bounded by one arch of the sine wave y = sin x and the x-axis. (a) (10 pts. ) Sketch the region r, showing a typical vertical rectangle. (b) (10 pts. ) Give the integral (do not evaluate) for the area of r. (c) (10 pts. ) Set up and evaluate the integral for the volume generated when. R is revolved about the x-axis. (d) (10 pts. ) Give the integral (do not evaluate) for the volume generated when r is revolved about the line x = 4: (10 pts. ) Give the integral (do not evaluate) for the area of the surface generated by revolving the curve x = 2t + 1 y = t2 + t. 0 t 2 about the x-axis. dx. Z cos3 x sin x = xdx: (10 pts. )
