New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2005 · Shift 0 · Q110

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2005 · Shift 0 · Q110

Definite Integration question

2005 · Shift 0 · Q110

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f:R \to R

be a differentiable function having

f\left( 2 \right) = 6

,

f'\left( 2 \right) = \left( {{1 \over {48}}} \right)

. Then

\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt}

equals :

A
$24$
B
$36$
C
$12$
D
$18$

More from Definite Integration

The value of $- π \int π \frac{c o s ^{2}}{1 + a ^{x}} d x, a > 0,$ is2005 · MCQ
If $I_{1} = 0 \int 1 2^{x^{2}} d x, I_{2} = 0 \int 1 2^{x^{3}} d x, I_{3} = 1 \int 2 2^{x^{2}} d x$ and $I_{4} = 1 \int 2 2^{x^{3}} d x$ then2005 · MCQ
The value of integral, $3 \int 6 \frac{x}{9 - x + x} d x$ is2005 · MCQ
The value of $I = 0 \int π /2 \frac{( s i n x + c o s x ) ^{2}}{1 + s i n 2 x} d x$ is2004 · MCQ
The value of $- 2 \int 3 1 - x^{2} d x$ is2004 · MCQ
If $0 \int π x f (sin x) d x = A 0 \int π /2 f (sin x) d x,$ then $A$ is2004 · MCQ
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