JEE Mains · Maths · STD 12 - 7.2 definite integral
Which of the following statements is incorrect for the function \(g(\alpha)\) for \(\alpha \in R\) such that \(g(\alpha)=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin ^{\alpha} x}{\cos ^{\alpha} x+\sin ^{\alpha} x} d x\)
- A \(g (\alpha)\) is a strictly increasing function
- B \(g (\alpha)\) has an inflection point at \(\alpha=-\frac{1}{2}\)
- C \(g (\alpha)\) is a strictly decreasing function
- D \(g (\alpha)\) is an even function
Answer & Solution
Correct Answer
(D) \(g (\alpha)\) is an even function
Step-by-step Solution
Detailed explanation
\(g(\alpha)=\int_{\frac{\pi}{6}}^{\pi / 3} \frac{\sin ^{\alpha} x}{\left(\sin ^{\alpha} x+\cos ^{\alpha} x\right)}\) \(.......(i)\) \(g(\alpha)=\int_{\frac{\pi}{6}}^{\pi / 3} \frac{\cos ^{\alpha} x}{\left(\sin ^{\alpha} x+\cos ^{\alpha} x\right)}\) \(.....(ii)\) \((1)+(2)\)…
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