Question 1Use the area interpretation to evaluate the definite integral11(1|x|)dx.Answer for Question 1You entered:PreviewHelpYour AnswerScoreExplanation

1Correct1.00

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The value of a definite integral is the area under the curve between the limits. (please provide answer as a numerical response.)Question 2Use the Fundamental Theorem of Calculus to evaluate the definite integral11(1|x|)dx. (please provide answer as a numerical response.)Answer for Question 2You entered:PreviewHelpYour AnswerScoreExplanation

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The value of the definite integralbaf(x)dxis equal toF(b)F(a)whereF(x)is a function such thatF(x)=f(x).Question 3FindTsuch thatT012x54dx=1. (please provide answer as a numerical response.)Answer for Question 3You entered:PreviewHelpYour AnswerScoreExplanation

6Correct1.00

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Evaluate the definite integral and then solve forT.Question 4Use integration by parts to compute the indefinite integralxsin(x)dx.Answer for Question 4You entered:PreviewHelpYour AnswerScoreExplanation

sin(x)-x*cos(x)+cCorrect1.00

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LetF(x)=xandg(x)=sin(x)and use the integration by parts formula.Question 5Use integration by substitution to evaluate the definite integral11x2cos(x3+3)dx. Express your answer using thesinfunction.Answer for Question 5You entered:PreviewHelpYour AnswerScoreExplanation

(1/3)*sin(4) - (1/3)*sin(2)Correct1.00

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Letu=x3+3thendu=3x2. The integral becomes1342cos(u)du.Question 6Find values ofaandbsuch thatx26x=(xa)2+b. Answer this question by entering exactly 2 numeric values separated by a space (the first corresponds toaand the second tob). (please provide answers as a numerical response.)Answer for Question 6You entered:

Your AnswerScoreExplanation

3Correct0.50

-9Correct0.50

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The left hand side is1x26x+0and the right hand side is1x22ax+(a2+b). Thus2a=6a=3and(a2+b)=32+b=0b=9.Question 7Find the derivative off(t)=t20exdx.Answer for Question 7You entered:PreviewHelpYour AnswerScoreExplanation

2*t*E^t^2Correct1.00

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Since the exponential function is its own antiderivativef(t)=et21. Thusf(t)=2tet2by the chain rule. This equivalent to the formula from topic 7.Question 8Compute11x2dx. (please provide answer as a numerical response.)Answer for Question 8You entered:PreviewHelpYour AnswerScoreExplanation

1Correct1.00

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Compute the definite integralb11x2dxusing the antipower rule then take the limit asb.Question 9Compute101xdx.Answer for Question 9You entered:PreviewHelpYour AnswerScoreExplanation

nanCorrect1.00

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For $$0Question 10Computeddx[xet2dt].Answer for Question 10You entered:PreviewHelpYour AnswerScoreExplanation

E^(-x^2)Correct1.00

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Using the formula in topic 10, this derivative is equivalent toddx[x0et2dt]which can be computed using the technique from topic 7.