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Class 12 Integrals · Conceptual Answer1 Marksindefinite_integration

Class 12 Maths · Integrals · Conceptual Answer #130

Evaluate \(\int \frac{1}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\,dx\). Work on each connected open interval where the real integrand is defined.

✅ Step-by-Step Solution

Final Answer: \(\tan{\left(x \right)} - \cot{\left(x \right)}\) + C
  1. Use 1/(sin²x cos²x)=sec²x+csc²x and integrate termwise to tan x−cot x+C.
  2. Therefore the required integral is \(\tan{\left(x \right)} - \cot{\left(x \right)}\) + C.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Use 1/(sin²x cos²x)=sec²x+csc²x and integrate termwise to tan x−cot x+C.
  • [0.5 marks] Therefore the required integral is \(\tan{\left(x \right)} - \cot{\left(x \right)}\) + C.

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