2019W2_MATH103_ALL.D6FEYB2NC501.Assignment_7.pdf - Stella...

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Stella Lin 2019W2 MATH103 ALL Assignment Assignment 7 due 03/03/2020 at 01:00am PST 1. (1 point) Which of the following is the correct form of the partial frac- tion decomposition of 2 x ( x + 3 )( 3 x + 1 ) ? x x 2 - 64 dx = Z dw w = ln | w | + C = ln | x 2 - 64 | + C . The properties of logarithms show that the two results are the same: ln | x + 8 | + ln | x - 8 | = ln | ( x + 8 )( x - 8 ) | = ln | x 2 - 64 | . A. Ax + B x + 3 + Cx + D 3 x + 1 B. A x + 3 + B 3 x + 1 C. Ax + B x + 3 + C 3 x + 1 D. A x + 3 + Bx + C 3 x + 1 Answer(s) submitted: B (correct) Correct Answers: B 2. (1 point) Using the substitution w = x 2 - 64, we get dw = 2 xdx , so we have Z 2 x x 2 - 64 dx = Z dw w = ln | w | + C = ln | x 2 - 64 | + C . The properties of logarithms show that the two results are the same: ln | x + 8 | + ln | x - 8 | = ln | ( x + 8 )( x - 8 ) | = ln | x 2 - 64 | .
Calculate the integral below by partial fractions and by using the indicated substitution. Be sure that you can show how the results you obtain are the same.
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xˆ3/3+2(lnabs(x+5)-lnabs(x+6))+C (correct) Correct Answers: xˆ3/3+2*ln(|x+5|)-2*ln(|x+6|)+C 4. (1 point) Calculate the integral below. Use C (capital C) for constant.
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