hw7 - jth734 Homework 7 Odell (58340) This print-out should...

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Unformatted text preview: jth734 Homework 7 Odell (58340) This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points 1. I = 4x2 4 - x2 dx . 2. I = 3. I = 4. I = 5. I = 003 10.0 points 1 Determine the integral I = 2 (x2 + 4) 2 3 dx . Evaluate the integral 2 I = 0 1. I = 2 2. I = 4 3. I = 2 -1 2 3 2 - 3 2 3 - 2 -1 2 3 - 3 2 4. I = 4 5. I = 2 6. I = 1 +C 2 x2 + 4 x +C 2 x2 + 4 x2 + 4 +C x x2 + 4 +C 2x x x2 + 4 +C 2 x +C x2 + 4 004 10.0 points 6. I = 2 -1 3 002 10.0 points x2 dx . (4 - x2 )3/2 x2 +C 2 x +C 2 x +C 2 Determine the indefinite integral I = 1. I = -4 ln x- 2. I = 3 ln x + 3. I = -4 ln x+ 4. I = 3 ln x + 5. I = 3 ln x - 005 3 - 4x dx . x2 - 1 x2 - 1 +3 x2 - 1 + 4 x2 - 1 -3 x2 - 1 - 4 x2 - 1 - 4 10.0 points x2 - 1 +C x2 - 1 + C x2 - 1+C x2 - 1 + C x2 - 1 + C Determine the integral I = x2 + sin-1 2 4-x x - sin-1 2. I = 4 - x2 x + sin-1 3. I = 2 4-x 1. I = 4. I = 5. I = 6. I = 2x x +C - sin-1 4 4 - x2 2x - sin-1 2 4 4-x x2 +C Which one of the following functions is an antiderivative of f when f (x) = x2 1 ? - 2x+ 2 x2 2x2 + sin-1 +C 4 4 - x2 jth734 Homework 7 Odell (58340) 1. F (x) = - 2 (x - 1) 2 - 2 x + 2)2 (x 3. - 4. 5. 2 x-2 2 2. F (x) = tan-1 (x - 1) 3. F (x) = ln x-2 x+1 1 x-2 3 x-2 4. F (x) = sin-1 (x - 1) 5. F (x) = ln(x2 - 2 x + 2) 006 10.0 points 6. - 1 x-2 008 10.0 points Find the unique function y satisfying the equations dy 3 = , dx (x - 3)(8 - x) 1. y = 2. y = 3. y = x-3 3 ln + ln 4 5 8-x y(4) = 0. Rewrite the expression f (x) = x2 (x - 3) 3x - 2 using partial fractions. 1. f (x) = - 2. f (x) = - 3. f (x) = 4. f (x) = 5. f (x) = 7 2 + 2 x x-3 7 2 7 + 2+ 9x 3x 9(x - 3) 8-x 3 - ln 4 ln 5 x-3 x-3 1 + ln 4 ln 5 8-x 8-x - ln 4 x-3 4. y = 3 ln 5. y = 3 ln 2 7 - 2 x x-3 2 7 7 - 2- 3x 9x 9(x - 3) 7 2 7 - 2+ x 3x 9(x - 3) 007 10.0 points x-3 + ln 4 8-x 10.0 points 009 Evaluate the integral 1 I = 0 4x dx . (x + 1)(x2 + 1) In the partial fractions decomposition of the expression f (x) = x3 - 2x + 5 , x2 - x - 2 2 2. I = ln 8 - 2 1. I = ln 2 + 3. I = 2 ln 2 + 2 4. I = 2 ln 8 - 2 5. I = 2 - ln 2 2 find the term having denominator x - 2. 1. 2 x-2 3 x-2 2. - jth734 Homework 7 Odell (58340) 6. I = - ln 2 2 010 10.0 points 1. I = 4 2. I = 2 3. I = 4 4. I = 1 5. I = 6. I = 2 013 10.0 points Evaluate the integral /2 3 I = /3 8 sin x dx . 1 + 4 cos2 x Evaluate the definite integral 4 x I = dx . 1 x - 16 1. I = 4 ln 9 -2 5 2. I = 2 - 4 ln 3 3. I = 1 - 4 ln 3 4. I = 2 - 4 ln 9 5 5. I = 4 ln 3 - 1 6. I = 4 ln 9 -1 5 10.0 points Evaluate the definite integral 1 011 I = 0 (4 + x)-1/2 dx . Evaluate the definite integral ln 2 I = 0 ex 5 dx . +3 1. I = 2. I = 1 5-2 4 1. I = 3 8 ln 5 5 2. I = 5 ln 2 3. I = 5 8 ln 3 5 1 5-1 4 3. I = 2 5 - 1 4. I = 5. I = 5-2 8 4. I = 5 ln 5 5. I = 5 ln 2 3 1 5-1 2 6. I = 2 5 - 2 014 10.0 points 3 6. I = ln 2 5 012 10.0 points Evaluate the integral /4 I = 0 sec2 x {2 - 3 sin x} dx . jth734 Homework 7 Odell (58340) 1. I = 5 + 3 2 2. I = 5 + 3. I = 4. I = 5. I = 6. I = 3 2 2 3 2 -1 - 2 3 -1 + 2 2 5-3 2 -1 - 3 2 015 10.0 points Find e9x dx . 81 + e18x 1 9x 1 +C arctan e 81 9 1 2. arcsec e9x + e9x + C 9 1. 3. None of these. 4. arcsin e9x + C 1 arcsin e9x + C 9 1 6. +C 9 + e9x 5. 018 +C +C +C 10.0 points 2. I = 4(4 - ) 3. I = 4(2 + ) 4. I = 2( - 2) 5. I = 4( - 2) 6. I = 2(4 + ) 017 10.0 points 4 Determine the indefinite integral I= 1 dx . 13 - 4x + x2 x-3 2 x-2 3 x+3 2 x+2 3 x+2 3 x-3 2 x-2 3 x+3 2 +C +C +C +C +C 1 1. I = tan-1 3 2. I = 1 tan-1 3 3. I = tan-1 4. I = tan-1 5. I = sin-1 6. I = 7. I = 1 -1 sin 3 1 -1 sin 3 Determine the integral I = 4x ln (2 + x) dx . 8. I = sin-1 016 1. I = 2(x2 - 4) ln (2 + x) + 4x - x2 + C 2. I = 2(x2 - 4) ln (2 + x) - 4x + x2 + C 3. I = 4. I = 1 1 2 (x - 4) ln (2 + x) - x - x2 + C 2 4 1 2 1 (x - 4) ln (2 + x) + x - x2 + C 2 4 10.0 points Evaluate the integral ln 2 I = 0 4 ex - 1 dx. 1. I = 2(4 - ) jth734 Homework 7 Odell (58340) 1 5. I = (x2 - 4) ln (2 + x) + 2x + x2 + C 2 1 6. I = (x2 - 4) ln (2 + x) + 2x - x2 + C 2 019 10.0 points 5 Determine the integral I = 2 sin-1 x dx . x 2 +C 1-x 1. I = 2x sin-1 x - 2 +C 2. I = 2 x sin-1 x + 1-x 3. I = 4 x sin-1 x - 4 1 - x + C 4. I = 4 x sin-1 x + 4 1 - x + C 5. I = 2x sin-1 x + 6. I = 4x sin-1 x + 2 +C 1-x 1-x+C ...
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