Exam 7: Principle of Integral Evaluation

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Evaluate Evaluate   . Use a CAS or calculator with integration capability. It may be necessary to make a substitution that converts the integral into one that can be integrated. . Use a CAS or calculator with integration capability. It may be necessary to make a substitution that converts the integral into one that can be integrated.

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Answer true or false. Answer true or false.   diverges. diverges.

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Evaluate Evaluate   . Use a CAS or calculator with integration capability. It may be necessary to make a substitution that converts the integral into one that can be integrated. . Use a CAS or calculator with integration capability. It may be necessary to make a substitution that converts the integral into one that can be integrated.

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Evaluate Evaluate   . .

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Answer true or false. Answer true or false.   =   = -1 = Answer true or false.   =   = -1 = -1

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Answer true or false. Answer true or false.   = 6.69 = 6.69

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Evaluate Evaluate   . .

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Evaluate Evaluate   . .

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Use the Endpaper Integral Table to evaluate the integral. Use the Endpaper Integral Table to evaluate the integral.

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Use n = 10 to approximate Use n = 10 to approximate   by the trapezoid rule. by the trapezoid rule.

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Use inequality (10) to find an upper bound on the magnitude of the error for the approximate value of Use inequality (10) to find an upper bound on the magnitude of the error for the approximate value of   found by the midpoint approximation using 10 subintervals. found by the midpoint approximation using 10 subintervals.

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Use n = 10 subdivisions to approximate the value of the integral Use n = 10 subdivisions to approximate the value of the integral   by the midpoint approximation. by the midpoint approximation.

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Evaluate Evaluate   = =

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Use Endpaper Tables to evaluate Use Endpaper Tables to evaluate   . .

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Find the arc length of the curve y = ln(x4) for 2 \le x \le 4.

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Use Endpaper Tables to evaluate Use Endpaper Tables to evaluate   . .

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Answer true or false. Answer true or false.   = 0 = 0

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Use n = 10 subdivisions to approximate the value of the integral Use n = 10 subdivisions to approximate the value of the integral   by the trapezoidal approximation. by the trapezoidal approximation.

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Evaluate Evaluate   . .

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Answer true or false. The area enclosed by Answer true or false. The area enclosed by   , y = 0, x = 0, x = 16 is   . , y = 0, x = 0, x = 16 is Answer true or false. The area enclosed by   , y = 0, x = 0, x = 16 is   . .

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