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Engineering Math II – Spring 2015 Name: Quiz #2 Section: 561 / 562 / 563 Directions. Read each problem carefully and work it out on a separate sheet of paper. Put a box around the choice you believe best answers the question. Turn in your work with this sheet of paper stapled on top. Problem 1 (5 pts). The base of a solid is the parabolic region between the graphs of y = 1 and y = x2 . Cross sections perpendicular to the y-axis are squares. Find the volume of the solid. (a) 4 3 (b) 2 (c) 1 (d) 1 3 (e) 3 Problem 2 (5 pts). Find the volume of the solid formed by rotating the region bounded by x = 0, y = ln(x), y = 0, and y = 2 about the y-axis. (a) π 4 e 2 (b) π 4 e 2 −1 (c) πe4 − 1 (d) π 2 (e) π 4 (e 2 − 1) MATH 152:561-563 – Spring 2015 Quiz #2 2 Problem 3 (5 pts). Which of the following represents the area between the curves y = and y = 6 on the interval from x = 1 to x = 4? R4 − 6 dx (a) 1 12 x (b) R2 (c) R4 (d) R 12 12 (e) R6 1 1 6− 12 x 6− 12 x y 3 3 dx + R 4 12 2 x 12 x − 6 dx dx − 1 dy 4− 12 y dy + R 12 12 6 y − 1 dy Problem 4 (5 pts). Find the area of the region bounded by y = cos(x), y = −1, x = 0 and x = π2 . (a) π (b) π 2 (c) 1 + π 2 (d) −1 + (e) π 2 +2 π 2