Which of the following statements is correct for the function g(α) for α R such that g(α) = ∫ (π)/6 ^((π)/3) (sin ^α x)/(cos ^α x + sin ^α x)dx

(A) g(α) is a strictly increasing function

(C) g(α) has an inflection point at α = - 1/2

(D) g(α) is a strictly decreasing function

Integral Calculus: JEE Main 2021 Mathematics question

JEE Main 2021 · 17 Mar, Morning shift · Q3402

JEE Main 202117 Mar, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Which of the following statements is correct for the function g(

\alpha

) for

\alpha

\in

R such that

g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx}

JEE Main 2021 Integral Calculus Question with Solution (17 Mar Morning shift, Q3402) | JEE Arc

JEE Main 2021 · 17 Mar, Morning shift · Q3402

JEE Main 202117 Mar, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Which of the following statements is correct for the function g(

\alpha

) for

\alpha

\in

R such that

g(\alpha ) = \int\limits_{{\pi \over 6}}^{{\pi \over 3}} {{{{{\sin }^\alpha }x} \over {{{\cos }^\alpha }x + {{\sin }^\alpha }x}}dx}