Q.24 - Integration
⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ ln A B = ∫ 0 1 ( x + 1 ) ln x x − 1 d x = ∫ − A A sin ∣ x ∣ + cos ∣ x ∣ d x
Find B .
The answer is 4.
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Outline for one solution: To solve the first integral, expand 1/(1+x) as a geometric series and use a special case of the Frullani integral. Then use the Wallis product to solve for A. Next, solve the second integral. Split the integral to remove the absolute values.