Two worthy integrals a. Let I1a2 = L _ 0 dx 11 + xa211 +
Chapter 7, Problem 88(choose chapter or problem)
Two worthy integrals a. Let I1a2 = L _ 0 dx 11 + xa211 + x22 , where a is a real number. Evaluate I1a2 and show that its value is independent of a. (Hint: Split the integral into two integrals over 30, 14 and 31, _2; then use a change of variables to convert the second integral into an integral over 30, 14.) b. Let f be any positive continuous function on 30, p>24. Evaluate L p>2 0 f 1cos x2 f 1cos x2 + f 1sin x2 dx. (Hint: Use the identity cos 1p>2 - x2 = sin x.) (Source: Mathematics Magazine 81, 2, Apr 2008)
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