The function f(x) = _ 0 ^ x _ | t| ( t + 1 2 ) dt

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The function

f(x) = \int_{0}^{x} \log_{|\sin t|} \left( \sin t + \frac{1}{2} \right) dt, \text{ where } x \in (0, 2\pi), \text{ then}

f(x)

strictly increases in the interval (1)

\left( \frac{\pi}{6}, \frac{5\pi}{6} \right)

(2)

\left( \frac{5\pi}{6}, 2\pi \right)

(3)

\left( \frac{\pi}{6}, \frac{7\pi}{6} \right)

(4)

\left( \frac{5\pi}{6}, \frac{7\pi}{6} \right)