Match List-I with List-II (Given that c

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

Match List-I with List-II (Given that c is an arbitrary constant)

List-I	List-II
(A) $\int\frac{dx}{\sqrt{a^2-x^2}}=$	(I) $\log_e\|x + \sqrt{x^2 – a^2}\| + c$
(B) $\int\sqrt{a^2-x^2} dx=$	(II) $\sin^{-1}\frac{x}{a} + c$
(C) $\int\sqrt{x^2 – a^2} dx =$	(III) $\frac{x}{a}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+c$
(D) $\int\frac{dx}{\sqrt{x^2-a^2}}=$	(IV) $\frac{x}{a}\sqrt{x^2-a^2}-\frac{a^2}{2}\log_e\|x + \sqrt{x^2 – a^2}\| + c$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (4) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)

List-I	List-II
(A) $\int\frac{dx}{\sqrt{a^2-x^2}}=$	(II) $\sin^{-1}\frac{x}{a} + c$
(B) $\int\sqrt{a^2-x^2} dx=$	(III) $\frac{x}{a}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+c$
(C) $\int\sqrt{x^2 – a^2} dx =$	(IV) $\frac{x}{a}\sqrt{x^2-a^2}-\frac{a^2}{2}\log_e\|x + \sqrt{x^2 – a^2}\| + c$
(D) $\int\frac{dx}{\sqrt{x^2-a^2}}=$	(I) $\log_e\|x + \sqrt{x^2 – a^2}\| + c$