MATH 172 Midterm: MATH 172 TAMU 172-Spring 18 Exam 2 1 Solutions
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0 x2 sin x dx. (a) (b) 2 (c) 2 + 4 (d) 2 4 (e) 0. Solution: d we use integration by parts, taking u = x2 and dv = sin x dx. Then du = dx and v = cos x, from which we have. Z x2 sin x dx = x2 cos x + 2z x cos x dx. We apply integration by parts again, with u = x, dv = cos x dx, and du = dx, v = sin x: Z x2 sin x dx = x2 cos x + 2(cid:20)x sin x z sin x dx(cid:21) . 0 x2 sin x dx = h x2 cos x + 2x sin x + 2 cos xi . = ( 2( 1) + 0 + 2( 1)) (0 + 0 + 2) = 2 4 . Solution: d we take x = 2 sec , and so dx = 2 sec tan d .
