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Definite Integration question

2021 · 17 Mar · Shift 1 · Q25
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  2. /JEE Main
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  4. /Definite Integration
  5. /2021 · 17 Mar · Shift 1 · Q25

Definite Integration question

2021 · 17 Mar · Shift 1 · Q25

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1
Which of the following statements is correct for the function g(α\alphaα) for α∈\alpha\inα∈ R such that g(α)=∫π6π3sin⁡αxcos⁡αx+sin⁡αxdxg(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx}g(α)=6π​∫3π​​cosαx+sinαxsinαx​dx
  1. A
    g(α)g(\alpha )g(α) is a strictly increasing function
  2. B
    g(α)g(\alpha )g(α) is an even function
  3. C
    g(α)g(\alpha )g(α) has an inflection point at α\alphaα=−12-{1 \over 2}−21​
  4. D
    g(α)g(\alpha )g(α) is a strictly decreasing function
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