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Use a u-substitution to evaluate the given definite integral

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Use a u-substitution to evaluate the definite integral of the function 1/{[tan(2*theta)]*[sec^2(2*theta)]} over the interval [pi/12, pi/6].

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A complete, detailed solution to the problem is provided, including reminders of a number of mathematical properties that enable us to get the solution. We first use a "test u-substitution'' and show that that one won't give us a u-integral in which we can immediately write down the antiderivative of the integrand. Then we proceed to a u-substitution that will permit us to immediately write down the antiderivative of the integrand.

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Georgia Martin, PhD
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  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
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