MAT 21A Study Guide - Midterm Guide: Trapezoidal Rule, Centroid, Numerical Analysis
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MAT 21A Full Course Notes
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Section: (5 points) evaluate the improper integral. 0 x2 e 3x dx: (5 points) evaluate. 2: (5 points) evaluate the inde nite integral. Z 2x 4 x2 x dx: (5 points) 3: (5 points) evaluate the de nite integral. 1: (5 points) evaluate the inde nite integral. 4: (10 points) find the centroid of the triangle bounded by the lines y = 6x, y = 6, y = x. 5: (20 points) let f (x) be a continuous function which satis es. 2 f (x) dx = y3 + c. 6: (20 points) this is a multi-part question. First nd the volume of the unbounded solid generated by rotating the curve y = x 2 from x = 1 to x = a, a > 1 about the x-axis. Second, nd the volume of the solid generated by rotating the same curve about the y-axis. Now take the limit as a . 7: (20 points) this is a multi-part question.
