Match List-I with List-II | List-I | List-II | | --- | --- | | Functions | Integrals | | --- | --- | | (A) dx/x^2 - 4, x ≠ ± 2 | (I) x + sqrt(4 + x^2) + C, where C is an arbitrary constant | | (B) 1sqrt(16 - x^2) dx; x < 4 | (II) ^-1 ( x/4 ) + C, where C is an arbitrary constant | | (C) 1/16 + x^2 dx | (III) 1/4 x-2/x+2 + C, where C is an arbitrary constant | | (D) 1sqrt(4 + x^2) dx | (IV) 1/4 ^-1 ( x/4 ) + C, where C is an arbitrary constant | Choose the correct answer from the options given below: Option 1: (A) - (IV), (B) - (III), (C) - (II), (D) - (I) Option 2: (A) - (III), (B) - (II), (C) - (IV), (D) - (I) Option 3: (A) - (III), (B) - (IV), (C) - (II), (D) - (I) Option 4: (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

The answer is '(A) - (III), (B) - (II), (C) - (IV), (D) - (I)'. View full solution:

Calculus > Integrals

Hard

core

Match List-I with List-II | List-I | List-II | | --- | --- | | Functions | Integrals | | --- | --- | | (A) $\int \frac{dx}{x^2 - 4}, x \neq \pm 2$ | (I) $\log \vert x + \sqrt{4 + x^2}\vert + C$, where $C$ is an arbitrary constant | | (B) $\int \frac{1}{\sqrt{16 - x^2}} dx; \vert x\vert < 4$ | (II) $\sin^{-1} \left( \frac{x}{4} \right) + C$, where $C$ is an arbitrary constant | | (C) $\int \frac{1}{16 + x^2} dx$ | (III) $\frac{1}{4} \log \left\vert \frac{x-2}{x+2} \right\vert + C$, where $C$ is an arbitrary constant | | (D) $\int \frac{1}{\sqrt{4 + x^2}} dx$ | (IV) $\frac{1}{4} \tan^{-1} \left( \frac{x}{4} \right) + C$, where $C$ is an arbitrary constant | Choose the correct answer from the options given below:

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (III), (B) - (II), (C) - (IV), (D) - (I)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (IV), (B) - (III), (C) - (I), (D) - (II)

✅ Correct Option: 2

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