Assertion : e^ ^ -1 x (1- x 1-x^ 2 ) d x=e^ ^ -1 x 1-x^ 2 +c Reason : e ^ g(x) (g^ ( x )…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
Assertion :
\(\int e^{\sin ^{-1} x}\left(1-\frac{x}{\sqrt{1-x^{2}}}\right) d x=e^{\sin ^{-1} x} \cdot \sqrt{1-x^{2}}+c\)
Reason : \(\int \mathrm{e}^{g(x)}\left(g^{\prime}(\mathrm{x}) f(\mathrm{x})+f^{\prime}(\mathrm{x})\right) \mathrm{dx}=\mathrm{e}^{\mathrm{g}(\mathrm{x})} f(\mathrm{x})+\mathrm{c}\)
\(\int e^{\sin ^{-1} x}\left(1-\frac{x}{\sqrt{1-x^{2}}}\right) d x=e^{\sin ^{-1} x} \cdot \sqrt{1-x^{2}}+c\)
Reason : \(\int \mathrm{e}^{g(x)}\left(g^{\prime}(\mathrm{x}) f(\mathrm{x})+f^{\prime}(\mathrm{x})\right) \mathrm{dx}=\mathrm{e}^{\mathrm{g}(\mathrm{x})} f(\mathrm{x})+\mathrm{c}\)
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(A) If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
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