Question

1. (2 points) Evaluate the integral below. Use a capital letter C to denote an arbitrary constant. 2x+4 512x+1)(2-1) dx Answer(s) submitted: • 21n (abs (x-1))-ln (abs (2x-1)) +C (incorrect) 2. (2 points) Evaluate the definite integral. r3 - 2x + 5 dx= x² – 3x+2 Answer(s) submitted: (incorrect) 3. (2 points) Evaluate the definite integral. 3y2 – 3y +6 y(y + 1)(y-3) Answer(s) submitted: Si y07136+3 dy = Generated by © Web Work, http://webwork.maa.org. Mathematical Association of America

Answer 1

Soll, 2x+4 2 da » I- da (2x+1)(x-1) Xt Q (22+1) (2-1) using partial fraction 142 A + B (2-1) (2x+1)(241) (2111) + 21+1 I- 2 X-1 I du I - 2 CH (4) de 28 tdk -- 31,5 as the 52 40(1211)- enllul) +c =a ln12-1). en (122+1) +C . ) substitute 2x+1 ada = du dx = du I Arg 5x-1 Solna I = 7² axts di X² 32+2 +X+3) dx - 31+2 Substitute 52-1 = (22-3)+22 I = (2x-34+ 13 2 da tada side + Side 1² 31+2 6 0 = 13 9.X-3 dxt 22-34+2 dx + freda + 13 de 2 2²3x+2 0 0 I dat 9x-3 22 +1 + 3 2 Låde + f&d .3x+2 0 0 I 2x-3 dx + 13 adx + 3dx no 1) dx + sådx 1-) :) x²3x+2 substitute x² 3x+2=4 ( 91 - 3)ola du

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