Exam 4 with Solution for Calculus I | MATH 1501, Exams of Calculus

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KEY Student Name and [ID Number MATH 1501 Test 4, Fall 2005, WTT 1. Define a fimcetion F(x) by z= 1 Fa) = [ Tent a a. The domain of Fe) is: Co po) ® b. Fe) = t+» x* by the Fundamental Theorem of Calculus - Version 2. @, at fov ath The function F(a) is strictly increasing since: FOO" THe > 0 v * Show that F(z) < 2 for all 2. , K Fuxd= So aed eSvraet Oe il ~ a =|- & = FoF bg +4) At = ARTA 4 3 2. The next four problems involve the region R in the plane bounded by y = sin w and the portion of the a-axis between 2 = 0 and « =. Use the disk method to set up (but do not evaluate) a 3 definite integral for the volume of the solid obtained when this region is revolved about the z-axis. A gx sta x KAO Se 3. Now use the shell method to set up (but do not evaluate) a definite integral for the solid obtained when F? is rotated about the y-axis.