New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Integration question

2018 · Shift 1 · Q24

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Advanced
Mathematics
Application of Integration
2018 · Shift 1 · Q24

Application of Integration question

2018 · Shift 1 · Q24

JEE AdvancedMathematicsApplication of IntegrationMultiple correct+4 / −1

Let f : [0,

\infty

)

\to

R be a continuous function such that

f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt}

for all x

\in

[0,

\infty

). Then, which of the following statement(s) is (are) TRUE?

A
The curve y = f(x) passes through the point (1, 2)
B
The curve y = f(x) passes through the point (2, $-$ 1)
C
The area of the region $\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \}$ is ${{\pi - 2} \over 4}$
D
The area of the region $\{ (x,y) \in [0,1] \times R:f(x) \le y \le \sqrt {1 - {x^2}} \}$ is ${{\pi - 1} \over 4}$

More from Application of Integration

A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F2 takes away the region which lies between the sides PQ and a curve of the form y = xn (n > 1). If…2018 · Numerical
If the line x = $α$ divides the area of region R = {(x, y) $\in$ R2 : x3 $\leq$ y $\leq$ x, 0 $\leq$ x $\leq$ 1} into two equal parts, then2017 · Multiple correct
Area of the region ${(x, y) \in R^{2} : y \geq ∣ x + 3 ∣, 5 y \leq x + 9 \leq 15}$ is equal to2016 · MCQ
Let $F (x) = x \int x^{2} + \frac{π}{6} 2 cos^{2} t (d t)$ for all $x \in R$ and $f : [0, \frac{1}{2}] \to [0, \infty]$ be a continuous function. For $a \in [0, \frac{1}{2}],$ …2015 · Numerical
Let $f : R \to R$ be a continuous odd function, which vanishes exactly at one point and $f (1) = \frac{1}{2.}$ Suppose that $F (x) = - 1 \int x f (t) d t$ for all $x \in [- 1, 2]$ …2015 · Numerical
Let $F : R \to R$ be a thrice differentiable function. Suppose that $F (1) = 0, F (3) = - 4$ and $F (x) < 0$ for all $x \in (\frac{1}{2}, 3) .$ Let $f (x) = x F (x)$ …2015 · Multiple correct
The area enclosed by the curves $y = sin x + cosx o l imi t s$ and $y = ∣ cos x - sin x ∣$ over the interval $[0, \frac{π}{2}]$ is2013 · MCQ
Let $S$ be the area of the region enclosed by $y = e^{- x^{2}}$ , $y = 0$ , $x = 0$ , and $x = 1$ ; then2012 · Multiple correct