Duration: 3:37

9 views

0

Let \( \mathrm{f}:[0, \infty) \rightarrow \mathbb{R} \) be a containuous function such that \( \mathrm{f}(\mathrm{x}) \)
P \( =1-2 x+\int_{0}^{x} e^{x-t} f(t) d t \) for all \( x \in[0, \infty) \). Then, which of the

W
following statement(s) is (are) TRUE? [JEE Advanced - 2018]
(a) The curve \( \mathrm{y}=\mathrm{f}(\mathrm{x}) \) passes through the point \( (1,2) \)
(b) The curve \( y=\mathrm{f}(\mathrm{x}) \) passes through the point \( (2,-1) \)
(c) The area of the region \( \{(x, y) \in[0,1] \times \mathbb{R}: f(x) \leq y \leq \)
\( \left.\sqrt{1-x^{2}}\right\} \) is \( \frac{\pi-2}{4} \)
(d) The area of the region \( \{(\mathrm{x}, \mathrm{y}) \in[0,1] \times \mathbb{R}: \mathrm{f}(\mathrm{x}) \leq \mathrm{y} \leq \)
\( \left.\sqrt{1-x^{2}}\right\} \) is \( \frac{\pi-1}{4} \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live