MHT CET · Maths · Indefinite Integration
\(\int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x}=\)
- A \(\tan x+\cot x+\mathrm{c}\), where c is the constant of integration.
- B \(\tan x-\cot x+\mathrm{c}\), where c is the constant of integration.
- C \(\tan x \cot x+\mathrm{c}, \quad\) where c is the constant of integration.
- D \(\tan x-\cot 2 x+c\), where \(c\) is the constant of integration.
Answer & Solution
Correct Answer
(B) \(\tan x-\cot x+\mathrm{c}\), where c is the constant of integration.
Step-by-step Solution
Detailed explanation
\(\int \frac{\mathrm{d} x}{\sin ^2 x \cos ^2 x} = \int \frac{\sin^2 x + \cos^2 x}{\sin ^2 x \cos ^2 x} \mathrm{d} x\) \(= \int \left( \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} \right) \mathrm{d} x\)
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