Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\sec^{\frac{2}{3}}xcosec^{\frac{4}{3}}xdx=\)

Options:

\(3^{\frac{6}{7}}-3^{\frac{6}{5}}\)

\(3^{\frac{7}{6}}-3^{\frac{5}{6}}\)

\(3^{\frac{3}{5}}-3^{\frac{3}{7}}\)

\(3^{\frac{5}{3}}-3^{\frac{7}{3}}\)

Correct Answer:

\(3^{\frac{7}{6}}-3^{\frac{5}{6}}\)

Explanation:

\(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\sec^{\frac{2}{3}}xcosec^{\frac{4}{3}}xdx=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{\sec^2x}{(\tan x)^\frac{4}{3}}dx\)

Then put \(\tan x=t\)