The integral $ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x $ is equal to

Question

The integral $ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x $ is equal to, $ 3^{\frac{7}{6}}-3^{\frac{5}{6}} $, $ 3^{\frac{4}{3}}-3^{\frac{1}{3}} $, $ 3^{\frac{5}{6}}-3^{\frac{2}{3}} $, $ 3^{\frac{5}{3}}-3^{\frac{1}{3}} $

MARKS App · Accepted Answer

I = ∫ π 6 π 3 sec 2 3 x cosec 4 3 x d x = ∫ π 6 π 3 sec 2 x tan 4 / 3 x d x Let tan x = t , sec 2 x d x = d t ⇒ I = ∫ 1 3 3 d t t 4 3 = t - 4 3 + 1 - 4 3 + 1 1 3 3 = - 3 1 3 1 6 - 3 1 6 = 3 7 6 - 3 5 6 .

Search any question & find its solution

Looking for more such questions to practice?