MATH 152 Midterm: MATH 152 TAMU 2010c Exam 1b Solutions
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Exam i version b solutions: b the sketch of the region is shown below. Use a partition of the y-axis, so the functions are x = y + 1 and x = y2 1. These functions intersect when y + 1 = y2 1, y2 y 2 = 0, (y 2)(y + 1) = 0, or y = 2, 1. 1(cid:18)(y + 1) (y2 1)(cid:19) dy: d integrate by parts with u = x2, dv = ex dx. Inte- grate by parts again with u = 2x, dv = ex dx. Then x2ex dx = x2ex 2xex dx. yields x2ex 2xex + 2ex dx = x2ex 2xex + 2ex + c: b partition along the y-axis. The slices are square prisms 2x 2x dy = 4x2 dy = 4y dy. 4y dy = 2y2(cid:12)(cid:12)(cid:12: a the force (weight) of the rope and weight after it has been pulled up x feet is f (x) =
