Math 152Workshop 6Spring 20111. The regionRis bounded below by thex-axis, bounded on the left by the linex= 1, boundedon the right by the linex= 2, and bounded above by the curvey=5 +xx2+ 4x+ 3.(a) Sketch the regionRand set up a definite integral that gives the area ofR. Then calculatethe integral in two ways:i. Approximatelyusing thefnInt(program in your calculator.ii. Exactlyusing the method of partial fractions.iii. Checkthat the two answers are “the same” (that is, find approximate values forthe result of the second method).(b) The regionRis rotated around thex-axis to generate a solid bodyB. SketchBand setup a definite integral that gives the volume ofB. Calculate the integral in two ways:i. Approximatelyusing thefnInt(program in your calculator.ii. Exactlyusing the method of partial fractions (be careful how you set this up – therearefourundetermined coefficients in the partial fraction decomposition).
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