Match List I with List II | List I | List II | |---|---| | A. $\int \frac{dx}{x^2 - a^2}$ is equal to | I. $\frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\log\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$ | | B. $\int \frac{dx}{\sqrt{x^2 + a^2}}$ is equal to | II. $\frac{1}{2a}\log\left\lvert \frac{x-a}{x+a}\right\rvert + C$ | | C. $\int \sqrt{a^2 - x^2} \, dx$ is equal to | III. $\frac{x}{2}\sqrt{a^2 - x^2} + \frac{a^2}{2}\sin^{-1}\frac{x}{a} + C$ | | D. $\int \sqrt{a^2 + x^2} \, dx$ is equal to | IV. $\log\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$ | Choose the correct answer from the options given below:

Correct Answer: C. A-II, B-IV, C-III, D-I

Match List I with List II | List I | List II | |---|---| | A. ∫ dx x^2 - a^2… - CUET UG 2022 Mathematics PYQ

CUET UG 2022 — Mathematics Calculus

2022mcqeasy

Match List I with List II

List I	List II
A. $\displaystyle \int \frac{dx}{x^2 - a^2}$ is equal to	I. $\frac{x}{2}\sqrt{x^2 + a^2} + \frac{a^2}{2}\log\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$
B. $\displaystyle \int \frac{dx}{\sqrt{x^2 + a^2}}$ is equal to	II. $\frac{1}{2a}\log\left\lvert \frac{x-a}{x+a}\right\rvert + C$
C. $\displaystyle \int \sqrt{a^2 - x^2} \, dx$ is equal to	III. $\frac{x}{2}\sqrt{a^2 - x^2} + \frac{a^2}{2}\sin^{-1}\frac{x}{a} + C$
D. $\displaystyle \int \sqrt{a^2 + x^2} \, dx$ is equal to	IV. $\log\left\lvert x + \sqrt{x^2 + a^2}\right\rvert + C$

Choose the correct answer from the options given below:

Official previous-year question

Held on 16 Jul 2022 · Verified 13 Jul 2026.

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