Question

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \, \csc^{\frac{4}{3}} x \, dx$ is equal to

• A. $3^{\frac{5}{6}}-3^{\frac{2}{3}}$
• B. $3^{\frac{7}{6}}-3^{\frac{5}{6}}$
• C. $3^{\frac{5}{3}}-3^{\frac{1}{3}}$
• D. $3^{\frac{4}{3}}-3^{\frac{1}{3}}$

Hint:

Calculus Tip: For integrals of the form $\int \sin^m x \cos^n x dx$, if $(m+n)$ is a negative even integer (here, $-4/3 - 2/3 = -2$), dividing the numerator and denominator by $\cos^{-(m+n)}x$ (here, $\cos^2 x$) is the standard technique to convert the expression into terms of $\tan x$ and $\sec^2 x$.

Answer 1

The Correct Option is B