New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2010 · Shift 1 · Q49

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

PYQ Library
JEE Advanced
Mathematics
Definite Integration
2010 · Shift 1 · Q49

Definite Integration question

2010 · Shift 1 · Q49

JEE AdvancedMathematicsDefinite IntegrationMCQ+4 / −1

The value of

\mathop {\lim }\limits_{x \to 0} {1 \over {{x^3}}}\int\limits_0^x {{{t\ln \left( {1 + t} \right)} \over {{t^4} + 4}}} dt

is

A
$0$
B
${1 \over 12}$
C
${1 \over 24}$
D
${1 \over 64}$

More from Definite Integration

Let $f$ be a real-valued function defined on the interval $(- 1, 1)$ such that $e^{- x} f (x) = 2 + 0 \int x t^{4} + 1 d t,$ for all $x \in (- 1, 1)$ , and let $f^{- 1}$ be the inverse…2010 · MCQ
Let $f : R \to R$ be a continuous function which satisfies $f (x) = 0 \int x f (t) d t$ . Then, the value of is .2009 · Numerical
If $I_{n} = - π \int π \frac{s i n n x}{( 1 + π ^{x} ) s i n x} d x, n = 0, 1, 2,$ .... then2009 · Multiple correct
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
Consider the function $f : (- \infty, \infty) \to (- \infty, \infty)$ defined by $f (x) = \frac{x ^{2} - a x + 1}{x ^{2} + a x + 1}, 0 < a < 2.$ Let $g (x) = 0 \int e^{x} \frac{f ^{'} ( t )}{1 + t ^{2}} d t .$ …2008 · MCQ
$x \to \frac{π}{4} lim \frac{2 \int s e c ^{2} x f ( t ) d t}{x ^{2} - \frac{π ^{2}}{16}}$ equal2007 · MCQ
Match the integrals in Column I with the values in Column II. Includes table2007 · MCQ
If $α = \frac{1}{2} \int 2 \frac{t a n ^{- 1} x}{2 x ^{2} - 3 x + 2} d x$ then the value of $7 tan (\frac{2 α 7}{π})$ is . (Here, the inverse trigonometric function $tan^{- 1} x$ …2025 · Numerical