MAT 286 Midterm: MAT286-2010Spring
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Qiang guo, wu-teh hsiang, patrick neary, marju purin, daniel van vliet. [5 points for each problem. ] (a) z (4x3 + 6x 5) dx (b) z 4e 3x dx. 3 (c) z x x2 + 5 dx (d) z x sin x dx. 4: for (a) and (b), nd the values of the de nite integrals. For (c) and (d), each of the improper integrals, determine if it converges or diverges, and nd the value of each that converges. [5 points for each problem. ] (a) z 8. 0 x x2 + 5 dx (d) z . 6: (a) find the average value of the function, f (x) = x + 1 , over the interval [3, 8]. [5 points] (b) find the volume under the given surface, and above the rectangle with the given boundaries, 2 6 x 6 2, 0 6 y 6 3. [5 points] f (x, y) = (cid:0)4 x2(cid:1) y,
