MAT 21B Study Guide - Midterm Guide: Exponential Growth, By2, Linear Density
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MAT 21B Full Course Notes
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Z (x2 + sin(x)) dx = (cid:18) 1. 3 ( 1) (0 1) = Z sec2(x) dx = tan(x) + c (standard integral) 2 sin(2x 1) + c (use substitution u = 2x 1) X dx (c) (d) (e) (f) dx = 2z (1 + x)7. + c (use the substitution u = x) 1 (ey + e y) dy (note: the answer is a function of b) (ey + e y) dy = (cid:0)ey e y(cid:1)(cid:12)(cid:12)(cid:12) b. = eb e b e + e 1. 2 (cid:0)e4 1(cid:1) (use the substitution u = x2) Question 2 compute the arc length of the curve y = x3/6 + 1/(2x) from x = 2 to x = 3. The arc length is given by r 3. First we simplify the integrand: y = x2. 2 p1 + (y )2 dx = z 3. 2x2(cid:19)2 (absolute value is redundant for 2 x 3).
