Question

Which of the following statements is incorrect for the function g(α) for α ∈ R such that

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

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

(2) g(α) has an inflection point at α = \(-\frac{1}{2}\)

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

(4) g(α) is an even function

Answer 1

Correct answer is (4)

Constant and even function

Due to typing mistake it must be bonus.