Let f:[0,\infty)\to\mathbb{R} be a continuous function such that f(x)=1-2x+\int^x_0e^{x-t}f(t)dt for all x∊[0,\infty).Then, which of the following statement(s) is (are) TRUE ? [JEE Adv 2018 P1]

The curve y=f(x) passes through the point (1,2)

The curve y=f(x) passes through the point (2,-1)

The area of the region \{(x,y)∊[0,1]\times\mathbb{R}:f(x) \leq y \leq \sqrt{1-x^2}\} is {\pi-2}/4

The area of the region \{(x,y)∊[0,1]\times\mathbb{R}:f(x) \leq y \leq \sqrt{1-x^2}\} is {\pi-1}/4

Application of Integration

Section: Mathematics

Question : 13 of 28

Marks: +1, -0

Let f:[0,∞)→ℝ be a continuous function such that f(x)=1−2x+∫0xex−tf(t)dt for all x∊[0,∞).Then, which of the following statement(s) is (are) TRUE ?

[JEE Adv 2018 P1]

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