Match List-I with List-II (Given that c is an arbitrary constant)
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List-I |
List-II |
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(A) $\int\frac{dx}{\sqrt{a^2-x^2}}=$ |
(I) $\log_e|x + \sqrt{x^2 – a^2}| + c$ |
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(B) $\int\sqrt{a^2-x^2} dx=$ |
(II) $\sin^{-1}\frac{x}{a} + c$ |
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(C) $\int\sqrt{x^2 – a^2} dx =$ |
(III) $\frac{x}{a}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+c$ |
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(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:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
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List-I |
List-II |
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(A) $\int\frac{dx}{\sqrt{a^2-x^2}}=$ |
(II) $\sin^{-1}\frac{x}{a} + c$ |
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(B) $\int\sqrt{a^2-x^2} dx=$ |
(III) $\frac{x}{a}\sqrt{a^2-x^2}+\frac{a^2}{2}\sin^{-1}\frac{x}{a}+c$ |
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(C) $\int\sqrt{x^2 – a^2} dx =$ |
(IV) $\frac{x}{a}\sqrt{x^2-a^2}-\frac{a^2}{2}\log_e|x + \sqrt{x^2 – a^2}| + c$ |
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(D) $\int\frac{dx}{\sqrt{x^2-a^2}}=$ |
(I) $\log_e|x + \sqrt{x^2 – a^2}| + c$ |