Exam 6: Techniques of Integration

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Evaluate the integral. Evaluate the integral.

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Evaluate the integral using the indicated trigonometric substitution. Evaluate the integral using the indicated trigonometric substitution.

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Find the integral. Find the integral.

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Find the integral. Find the integral.

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Use the Table of Integrals to evaluate the integral. Use the Table of Integrals to evaluate the integral.

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Find the integral. Find the integral.

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Find the integral. Find the integral.

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Evaluate the integral. Evaluate the integral.

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Find the integral. Find the integral.

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Find the integral. Find the integral.

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Evaluate the integral. Evaluate the integral.

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Determine whether the improper integral converges or diverges,and if it converges,find its value. Determine whether the improper integral converges or diverges,and if it converges,find its value.

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Use the Table of Integrals to evaluate the integral to three decimal places. Use the Table of Integrals to evaluate the integral to three decimal places.

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Find the integral. Find the integral.

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Evaluate the following integralEvaluate the following integral

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Evaluate the integral. Evaluate the integral.

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Evaluate the integral or show that it is divergent. Evaluate the integral or show that it is divergent.

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Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.  over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer. Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz).The voltage is thus given by the function E(t),where t is the time in seconds.Voltmeters read the RMS (root-mean-square)voltage,which is the square root of the average value of   over one cycle.Calculate the RMS voltage of household current.Round your answer to the nearest integer.

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Make a substitution to express the integrand as a rational function and then evaluate the integral. Make a substitution to express the integrand as a rational function and then evaluate the integral.   Round the answer to four decimal places. Round the answer to four decimal places.

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Evaluate the integral using integration by parts with the indicated choices of u and dv. Evaluate the integral using integration by parts with the indicated choices of u and dv.

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