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Definite Integration question

2016 · 9 Apr · Shift 1 · Q42
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  5. /2016 · 9 Apr · Shift 1 · Q42

Definite Integration question

2016 · 9 Apr · Shift 1 · Q42

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1
If 2∫01tan⁡−1xdx=∫01cot⁡−1(1−x+x2)dx,2\int\limits_0^1 {{{\tan }^{ - 1}}xdx = \int\limits_0^1 {{{\cot }^{ - 1}}} } \left( {1 - x + {x^2}} \right)dx,20∫1​tan−1xdx=0∫1​cot−1(1−x+x2)dx, then ∫01tan⁡−1(1−x+x2)dx\int\limits_0^1 {{{\tan }^{ - 1}}} \left( {1 - x + {x^2}} \right)dx0∫1​tan−1(1−x+x2)dx is equalto :
  1. A
    log4
  2. B
    π2{\pi \over 2}2π​ + log2
  3. C
    log2
  4. D
    π2−{\pi \over 2}-2π​− log4
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