New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Application of Integration question

2012 · Shift 1 · Q33

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

PYQ Library
JEE Advanced
Mathematics
Application of Integration
2012 · Shift 1 · Q33

Application of Integration question

2012 · Shift 1 · Q33

JEE AdvancedMathematicsApplication of IntegrationMultiple correct+4 / −1

Let

S

be the area of the region enclosed by

y = {e^{ - {x^2}}}

,

y=0

,

x=0

, and

x=1

; then

A
$S \ge {1 \over e}$
B
$S \ge 1 - {1 \over e}$
C
$S \le {1 \over 4}\left( {1 + {1 \over {\sqrt e }}} \right)$
D
$S \le {1 \over {\sqrt 2 }} + {1 \over {\sqrt e }}\left( {1 - {1 \over {\sqrt 2 }}} \right)$

More from Application of Integration

Let the straight line $x = b$ divide the area enclosed by $y = (1 - x)^{2}, y = 0,$ and $x = 0$ into two parts $R_{1} (0 \leq x \leq b)$ and $R_{2} (b \leq x \leq 1)$ such that $R_{1} - R_{2} = \frac{1}{4} .$ …2011 · MCQ
Let f $:$ $[- 1, 2] \to [0, \infty]$ be a continuous function such that $f (x) = f (1 - x)$ for all $x \in [- 1, 2]$ Let $R_{1} = - 1 \int 2 x f (x) d x,$ …2011 · MCQ
Let $f$ be a real-valued function defined on the interval $(0, \infty)$ by $f (x) = ln x + 0 \int x 1 + sin t d t .$ then which of the following statement(s) is (are) true?2010 · Multiple correct
Consider the polynomial $f (x) = 1 + 2 x + 3 x^{2} + 4 x^{3} .$ Let $s$ be the sum of all distinct real roots of $f (x)$ and let $t = ∣ s ∣ .$ The area bounded by the curve $y = f (x)$ and the lines $x = 0, y = 0$ and $x = t,$ …2010 · MCQ
Area of the region bounded by the curve $y = e^{x}$ and lines $x = 0$ and $y = e$ is2009 · Multiple correct
Let $f$ be a non-negative function defined on the interval $0 \int x 1 - (f^{'} (t))^{2} d t = 0 \int x f (t) d t, 0 \leq x \leq 1$ . If $0 \int x 1 - (f^{'} (t))^{2} d t = 0 \int x f (t) d t, 0 \leq x \leq 1$ , and $f (0) = 0$ , then2009 · MCQ
Consider the functions defined implicitly by the equation $y^{3} - 3 y + x = 0$ on various intervals in the real line. If $x \in (- \infty, - 2) \cup (2, \infty)$ , the equation implicitly defines a unique real valued differentiable function $y = f (x)$ . If $x \in (- 2, 2)$ …2008 · MCQ
The area of the region between the curves $y = \frac{1 + s i n x}{c o s x}$ and $y = \frac{1 - s i n x}{c o s x}$ bounded by the lines $x = 0$ and $x = \frac{π}{4}$ is2008 · MCQ