1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
Let $$f:R \to R$$ be a function defined by
$$f\left( x \right) = \left\{ {\matrix{ {\left[ x \right],} & {x \le 2} \cr {0,} & {x > 2} \cr } } \right.$$ where $$\left[ x \right]$$ is the greatest integer less than or equal to $$x$$, if $$I = \int\limits_{ - 1}^2 {{{xf\left( {{x^2}} \right)} \over {2 + f\left( {x + 1} \right)}}dx,} $$ then the value of $$(4I-1)$$ is
$$f\left( x \right) = \left\{ {\matrix{ {\left[ x \right],} & {x \le 2} \cr {0,} & {x > 2} \cr } } \right.$$ where $$\left[ x \right]$$ is the greatest integer less than or equal to $$x$$, if $$I = \int\limits_{ - 1}^2 {{{xf\left( {{x^2}} \right)} \over {2 + f\left( {x + 1} \right)}}dx,} $$ then the value of $$(4I-1)$$ is
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2
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
The value of $$\int\limits_0^1 {4{x^3}\left\{ {{{{d^2}} \over {d{x^2}}}{{\left( {1 - {x^2}} \right)}^5}} \right\}dx} $$ is
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3
IIT-JEE 2010 Paper 1 Offline
Numerical
+3
-0
For any real number $$x,$$ let $$\left[ x \right]$$ denote the largest integer less than or equal to $$x.$$ Let $$f$$ be a real valued function defined on the interval $$\left[ { - 10,10} \right]$$ by
$$$f\left( x \right) = \left\{ {\matrix{
{x - \left[ x \right]} & {if\left[ x \right]is\,odd,} \cr
{1 + \left[ x \right] - x} & {if\left[ x \right]is\,even} \cr
} } \right.$$$
Then the value of $${{{\pi ^2}} \over {10}}\int\limits_{ - 10}^{10} {f\left( x \right)\cos \,\pi x\,dx} $$ is
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4
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
Let $$f:R \to R$$ be a continuous function which satisfies $$f(x) = \int\limits_0^x {f(t)dt} $$. Then, the value of $$f(\ln 5)$$ is ____________.
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Questions Asked from Definite Integration (Numerical)
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