a Use a CAS to evaluate where n is an arbitrary positive integer Does your CAS find the result b In succession, find the integral when n 1, 2, 3, 5, and 7 Comment on the complexity of the results c Now substitute x ( 2) u and add the new and old integrals What is the value of This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS 0 2 sin x sin x cos x dx

Question: a. Use a CAS to evaluate where n is an arbitrary positive integer. Does your CAS find the result? b. In succession, find the integral

a. Use a CAS to evaluate 0 /2 sin" x sin" x + cos" x dx

where n is an arbitrary positive integer. Does your CAS find the result?

b. In succession, find the integral when n = 1, 2, 3, 5, and 7. Comment on the complexity of the results.

c. Now substitute x = (π/2) - u and add the new and old integrals. What is the value of

This exercise illustrates how a little mathematical ingenuity solves a problem not immediately amenable to solution by a CAS.

0 /2 sin" x sin" x + cos" x dx

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ANSWER a Using a CAS we can evaluate the integral as follows integrate sinn xsinn x cosn x dx from 0 to pi 2 Lets substitute sinx t then cosx dx dt sq... View full answer

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