Match List-I with List-II
| List-I | List-II | ||
| (A) | $∫\frac{dx}{a^2-x^2}$ | (I) | $\frac{1}{2a}log\left|\frac{x-a}{x+a}\right|+C$ |
| (B) | $∫\frac{dx}{x^2-a^2}$ | (II) | $\frac{1}{2a}log\left|\frac{a+x}{a-x}\right|+C$ |
| (C) | $∫\frac{dx}{x^2+a^2}$ | (III) | $sin^{-1}(\frac{x}{a})+C$ |
| (D) | $∫\frac{dx}{\sqrt{a^2-x^2}}$ | (IV) | $\frac{1}{a}tan^{-1}\frac{x}{a}+C$ |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(A) $∫\frac{dx}{a^2-x^2}⇒\frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+C$ (II)
(B) $∫\frac{dx}{x^2-a^2}⇒\frac{1}{2a}\log\left|\frac{x-a}{x+a}\right|+C$ (I)
(C) $∫\frac{dx}{x^2+a^2}⇒\frac{1}{a}\tan^{-1}\frac{x}{a}+C$ (IV)
(D) $∫\frac{dx}{\sqrt{a^2-x^2}}⇒\sin^{-1}\frac{x}{a}+C$ (III)