JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral \(\displaystyle\int_{\pi/6}^{\pi/3} \left(\dfrac{4 - \csc^2 x}{\cos^4 x}\right) dx\) is:
- A \(\dfrac{11}{\sqrt{3}}\)
- B \(\dfrac{16}{\sqrt{3}}\)
- C \(\dfrac{32}{3\sqrt{3}}\)
- D \(\dfrac{64}{3\sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{32}{3\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
The given integral is \(I = \displaystyle\int_{\pi/6}^{\pi/3} \left(\dfrac{4 - \csc^2 x}{\cos^4 x}\right) dx\). We can rewrite the integrand in terms of \(\tan x\) and \(\sec x\). Using the identity \(\csc^2 x = 1 + \cot^2 x = 1 + \dfrac{1}{\tan^2 x}\), we get:…
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