MATH 1120 Midterm: MATH 1120 Cornell pexam21sol
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Please show your reasoning and all your work. 2 (cos (u v) + cos (u + v)) 2 (cos (u v) cos (u + v)) Error m (b a)3 n and m is an upper bound of |f (x)| on [a, b]. + 2yn 2 + 4yn 1 + yn) where h = b a n and m is an upper bound of |f (iv)(x)| on [a, b]. Problem 1) (35 points) evaluate the following: (and please don"t forget the "+c". ) 1a) (5 points) z x sin (5x) dx. Solution: using ibp, u = x, du = dx, v = 1. Z x sin (5x) dx =z udv = uv z vdu. Z 1 x cos 5x + cos 5x dx sin 5x. Z sin5 x dx =z sin4 x sin xdx. =z (1 cos2 x)2 sin xdx (substitution u = cos x) =z (1 u2)2( 1)du =z ( u4 + 2u2 1)dx.
