JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(\int_{\pi /6}^{\pi /3} {{{\sec }^{2/3}}\,x\,\,\cos e{c^{4/3}}\,x\,dx} \) is equal to
- A \({3^{5/6}}\, - \,{3^{2/3}}\)
- B \({3^{5/3}}\, - \,{3^{1/3}}\)
- C \({3^{7/6}}\, - \,{3^{5/6}}\)
- D \({3^{4/3}}\, - \,{3^{1/3}}\)
Answer & Solution
Correct Answer
(C) \({3^{7/6}}\, - \,{3^{5/6}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \frac{1}{\cos ^{2 / 3} x \sin ^{1 / 3} x \cdot \sin x} d x\) \(=\int \frac{\tan ^{2 / 3} x}{\tan ^{2} x} \cdot \sec ^{2} x \cdot d x\) \(=\int \frac{\sec ^{2} x}{\tan ^{4 / 3} x} \cdot d x \quad\left\{\tan x=t, \sec ^{2} x d x=d t\right\}\)…
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