MATH138 Lecture 8: Midterm Review
23 Feb 2016
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Math 138 - winter 2016 - midterm review. Compute the following inde nite integrals. (a) z ln( x)dx (b) z x sin3 xdx (c) z x5 + x 1 (d) z tan5 x sec3 xdx (e) z. 1 + x2 x3 + 1 dx dx x3. 0 (a) z 7 (b) z 1 (c) z (d) z . X dx sin2 x x4 + 1 dx. Solve the following di erential equations. (a) dy dx y x. = x ln x (b) y = xy sin x y + 1. Problem 5. (a) the air in a room with volume 100 m3 contains 0. 15% co2 initially. The mixed air ows out at the same with 0. 05% co2 ows into the room at 2 m3 rate. How much co2 is in the room at time t? (b) suppose that a forest has 100 bears initially. After one year, the population of bears has grown to 120.
