MATH 1120 Midterm: MATH 1120 Cornell pexam1sol
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Please show your reasoning and all your work. Problem 1) (20 points) calculate the following: dx. 2x2 4 cos2 x sin x dx. Solution: letting u = 2x2 4, we have du = 4x dx and. 4z du ln|u| + c ln|2x2 4| + c. 4: one can either systematically do u = cos x or just eyeball: 0 cos2 x sin x dx = cos3 x. 1: letting u = x 1, we have du = dx and x(x 1)7 dx = z 2. 1 (u + 1)u7 du u8 + u7 du u9. 8: note that the recommended way to di erentiate or integrate 2x is to recognize it as being. Now letting u = 3 + 2x, we have du = (ln 2)(ex ln 2) dx = (ln 2)2x dx and. 1 ln 2 ln|u| + c ln (3 + 2x) ln 2.
