# Correct answers 62lnabss 1s 2lnabss 1 1s 1cc 5 1 pt

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Correct Answers:6*(2*ln(abs(s))-1/s-2*ln(abs(s-1))-1/(s-1))+C+c5.(1 pt) Evaluate the integral.Z-40ex-180e2x+13ex+36dxAnswer:+CHint: letu=exso thatdu=exdxand thusdx=du/u. Thissubstitution converts the integrand into a rational function inu,which can be integrated after partial fraction decomposition.Correct Answers:-5*x+1*ln(4+(eˆx))+4*ln(9+(eˆx))
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6.(1 pt)Make a substitution to express the integrand as a rationalfunction and then evaluate the integralZ10-21+3xdx10.(1 pt)Letf(x) =cos(x2).Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to ap-proximate the integralR10f(x)dxwithn=8. Give each answercorrect to six decimal places.T8=
7.(1 pt) Evaluate the integral.(c) Use the fact that|f00(x)| ≤6 on the interval[0,1]to esti-mate the errors in the approximations from part (a). Give eachanswer correct to six decimal places.
Correct Answers:0.3376469012061948.(1 pt) Use Simpson’s Rule to estimate the value of theintegralZ11f(x)dx.
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9.(1 pt) Given the following integral and value of n, approx-imate the following integral using the methods indicated (roundyour answers to six decimal places):
(a)Trapezoidal Rule(b)Midpoint Rule(c)Simpson’s Rule

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Term
Fall
Professor
MalabikaPramanik
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