New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2004 · Shift 0 · Q86

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2004 · Shift 0 · Q86

Definite Integration question

2004 · Shift 0 · Q86

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

If

\int\limits_0^\pi {xf\left( {\sin x} \right)dx = A\int\limits_0^{\pi /2} {f\left( {\sin x} \right)dx,} }

then

A

is

A
$2\pi$
B
$\pi$
C
${\pi \over 4}$
D
$0$

More from Definite Integration

If $f (x) = \frac{e ^{x}}{1 + e ^{x}}, I_{1} = f (- a) \int f (a) xg {x (1 - x)} d x$ and $I_{2} = f (- a) \int f (a) g {x (1 - x)} d x,$ …2004 · MCQ
If $f (y) = e^{y}, g (y) = y; y > 0$ and $F (t) = 0 \int t f (t - y) g (y) d y,$ then :2003 · MCQ
The value of $x \to 0 lim \frac{0 \int x ^{2} s e c ^{2} t d t}{x s in x}$ is2003 · MCQ
Let $f (x)$ be a function satisfying $f^{'} (x) = f (x)$ with $f (0) = 1$ and $g (x)$ be a function that satisfies $f (x) + g (x) = x^{2}$ . Then the value of the integral $0 \int 1 f (x) g (x) d x,$ …2003 · MCQ
If $f (a + b - x) = f (x)$ then $a \int b x f (x) d x$ is equal to2003 · MCQ
The value of the integral $I = 0 \int 1 x (1 - x)^{n} d x$ is2003 · MCQ
If $y = f (x)$ makes + $0$ intercept of $2$ and $0$ unit on $x$ and $y$ axes and encloses an area of $3/4$ square unit with the axes then $0 \int 2 x f^{'} (x) d x$ is2002 · MCQ
$I_{n} = 0 \int π /4 tan^{n} x d x$ then $n \to \infty lim n [I_{n} + I_{n + 2}]$ equals2002 · MCQ