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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

If the value of the definite integral ∫_ -1 ^1 ^ -1 ( 1 1 - x^2 ) (...

If the value of the definite integral ∫−11cot⁡−1(11−x2)(cot⁡−1x1−x2)∣x∣dx=π2(a−b)c\int_{-1}^1 \cot^{-1} \left( \frac{1}{\sqrt{1 - x^2}} \right) \left( \cot^{-1} \frac{x}{\sqrt{1 - x^2}} \right) |x| dx = \frac{\pi^2(\sqrt{a} - \sqrt{b})}{\sqrt{c}} where a,b,c∈Na, b, c \in N in their lowest form, then find the value of (a+b+c)(a + b + c).

Correct answer

7

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