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} $

Question

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} $

$g(\alpha )$ is a strictly increasing function

$g(\alpha )$ is an even function

$g(\alpha )$ has an inflection point at $\alpha$ = $-$${1 \over 2}$

$g(\alpha )$ is a strictly decreasing function

Solution

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