Match List-I with List-II | List-I | List-II | | --- | --- | | Integral | Solution: C is an arbitrary constant | | --- | --- | | (A) dx/x^2 + 25 | (I) 1/10 5 + x/5 - x + C | | (B) dx/x^2 - 25 | (II) x + sqrt(x^2 - 25) + C | | (C) dx/25 - x^2 | (III) 1/5 ^-1 ( x/5 ) + C | | (D) dxsqrt(x^2 - 25) | (IV) 1/10 x - 5/x + 5 + C | Choose the correct answer from the options given below: Option 1: (A) - (I), (B) - (IV), (C) - (III), (D) - (III) Option 2: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) Option 3: (A) - (IV), (B) - (III), (C) - (I), (D) - (II) Option 4: (A) - (II), (B) - (IV), (C) - (I), (D) - (III)

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

Calculus > Integrals

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Match List-I with List-II | List-I | List-II | | --- | --- | | Integral | Solution: C is an arbitrary constant | | --- | --- | | (A) $\int \frac{dx}{x^2 + 25}$ | (I) $\frac{1}{10} \log \left\vert \frac{5 + x}{5 - x} \right\vert + C$ | | (B) $\int \frac{dx}{x^2 - 25}$ | (II) $\log \vert x + \sqrt{x^2 - 25}\vert + C$ | | (C) $\int \frac{dx}{25 - x^2}$ | (III) $\frac{1}{5} \tan^{-1} \left( \frac{x}{5} \right) + C$ | | (D) $\int \frac{dx}{\sqrt{x^2 - 25}}$ | (IV) $\frac{1}{10} \log \left\vert \frac{x - 5}{x + 5} \right\vert + C$ | Choose the correct answer from the options given below:

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

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

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

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

✅ Correct Option: 2

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	LIST-I		LIST-II
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B.	$\displaystyle\int \dfrac{dx}{\sqrt{a^2 - x^2}}$	II.	$\log_e \vert x + \sqrt{x^2 - a^2} \vert + C$
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