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Integrals — ISC Class 12

Master Integrals for ISC Class 12. Free verified step-by-step solutions, 3 past exam problems, formulas, and markschemes.

Exam Questions & Step-by-Step Markschemes (3 Problems)

Question 1 • 2024 6 Marks
Evaluate: I = \int_{0}^{\pi/2} \log(\sin x) \, dx .
Answer: I = -\frac{\pi}{2} \log 2 = \frac{\pi}{2} \log\left(\frac{1}{2}\right)
Question 2 • 2023 4 Marks
Evaluate the indefinite integral: \int x \arctan x \, dx
Answer: \frac{x^2 + 1}{2} \arctan x - \frac{x}{2} + C
Question 3 • 2023 4 Marks
Evaluate: \int x \tan^{-1} x \, dx
Answer: \frac{1}{2}(x^2 + 1)\tan^{-1} x - \frac{x}{2} + C

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