Match List-I with List-II (where c is an arbitrary constant) | List-I | List-II | | --- | --- | | (A) x dx | (I) x + x + c | | (B) x dx | (II) x + c | | (C) x dx | (III) x + c | | (D) x dx | (IV) x - x + c | Choose the correct answer from the options given below: Option 1: (A) - (II), (B) - (IV), (C) - (I), (D) - (III) Option 2: (A) - (III), (B) - (II), (C) - (IV), (D) - (I) Option 3: (A) - (II), (B) - (III), (C) - (I), (D) - (IV) Option 4: (A) - (III), (B) - (IV), (C) - (II), (D) - (I)

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

Calculus > Integrals

Medium

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Match List-I with List-II (where $c$ is an arbitrary constant) | List-I | List-II | | --- | --- | | (A) $\int \tan x \, dx$ | (I) $\log\vert \sec x + \tan x\vert + c$ | | (B) $\int \cot x \, dx$ | (II) $\log\vert \sec x\vert + c$ | | (C) $\int \sec x \, dx$ | (III) $\log\vert \sin x\vert + c$ | | (D) $\int \cosec x \, dx$ | (IV) $\log\vert \cosec x - \cot x\vert + c$ | Choose the correct answer from the options given below:

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

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

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

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

✅ Correct Option: 3

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Match List-I with List-II

List-I	List-II
Indefinite integral	Solution (where 'c' is an arbitrary constant)
(A) $\displaystyle\int \sqrt{x^2-a^2} \, dx$	(I) $\dfrac{1}{a}\tan^{-1}\dfrac{x}{a} + c$
(B) $\displaystyle\int \dfrac{1}{x^2-a^2} \, dx$	(II) $\dfrac{x}{2}\sqrt{x^2+a^2} + \dfrac{a^2}{2}\log\left[x+\sqrt{x^2+a^2}\right] + c$
(C) $\displaystyle\int \dfrac{1}{x^2+a^2} \, dx$	(III) $\dfrac{x}{2}\sqrt{x^2-a^2} - \dfrac{a^2}{2}\log\left[x+\sqrt{x^2-a^2}\right] + c$
(D) $\displaystyle\int \sqrt{x^2+a^2} \, dx$	(IV) $\dfrac{1}{2a}\log\left\vert \dfrac{x-a}{x+a} \right\vert + C$

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