Statement - 1: _ 0 ^ ^ 2 x ^ -1 t d t+ _ 0 ^ cas ^ 2 x ^ -1 t d t= 4 for all x. Statement…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Statement - 1: \(\int_{0}^{\sin ^{2} x} \sin ^{-1} \sqrt{t} d t+\int_{0}^{\operatorname{cas}^{2} x} \cos ^{-1} \sqrt{t} d t=\frac{\pi}{4}\) for all x.
Statement - 2: \(\frac{d}{d x} \int_{\phi^{\prime}(x)}^{\psi|x|} f(t) d t=\psi^{\prime}(x) f(\psi(x))-\Phi^{\prime}(x) f(\Phi(x))\)
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true and Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(A) Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
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