Duration: 3:49

8 views

0

Let \( \mathrm{f}:[0,2] \rightarrow \mathrm{R} \) be a function which is continuous on \( [0,2] \) and is differentiable on \( (0,2) \) with \( f(0)=1 \). Let
P \( F(x)=\int_{0}^{x^{2}} f(\sqrt{t}) d t \) for \( \mathrm{x} \in[0,2] \). If \( F^{\prime}(\mathrm{x})=\mathrm{f}^{\prime}(\mathrm{x}) \) for all \( \mathrm{x} \in \) \( (0,2) \), then \( \mathrm{F}(2) \) equals
[JEE Advanced- 2014]
(a) \( \mathrm{e}^{2}-1 \)
(b) \( \mathrm{e}^{4}-1 \)
(c) \( \mathrm{e}-1 \)
(d) \( \mathrm{e}^{4} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live