1
JEE Advanced 2021 Paper 2 Online
Numerical
+2
-0
Let $${g_i}:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R,i = 1,2$$, and $$f:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R$$ be functions such that $${g_1}(x) = 1,{g_2}(x) = |4x - \pi |$$ and $$f(x) = {\sin ^2}x$$, for all $$x \in \left[ {{\pi \over 8},{{3\pi } \over 8}} \right]$$. Define $${S_i} = \int\limits_{{\pi \over 8}}^{{{3\pi } \over 8}} {f(x).{g_i}(x)dx} $$, i = 1, 2
The value of $${{48{S_2}} \over {{\pi ^2}}}$$ is ___________.
The value of $${{48{S_2}} \over {{\pi ^2}}}$$ is ___________.
Your input ____
2
JEE Advanced 2021 Paper 2 Online
Numerical
+4
-0
For any real number x, let [ x ] denote the largest integer less than or equal to x. If $$I = \int\limits_0^{10} {\left[ {\sqrt {{{10x} \over {x + 1}}} } \right]dx} $$, then the value of 9I is __________.
Your input ____
3
JEE Advanced 2020 Paper 2 Offline
Numerical
+4
-0
Let $$f:R \to R$$ be a differentiable function such that its derivative f' is continuous and f($$\pi $$) = $$-$$6.
If $$F:[0,\pi ] \to R$$ is defined by $$F(x) = \int_0^x {f(t)dt} $$, and if $$\int_0^\pi {(f'(x)} + F(x))\cos x\,dx$$ = 2
then the value of f(0) is ...........
If $$F:[0,\pi ] \to R$$ is defined by $$F(x) = \int_0^x {f(t)dt} $$, and if $$\int_0^\pi {(f'(x)} + F(x))\cos x\,dx$$ = 2
then the value of f(0) is ...........
Your input ____
4
JEE Advanced 2019 Paper 2 Offline
Numerical
+3
-0
The value of the integral $$ \int\limits_0^{\pi /2} {{{3\sqrt {\cos \theta } } \over {{{(\sqrt {\cos \theta } + \sqrt {\sin \theta } )}^5}}}} d\theta $$ equals ..............
Your input ____
Questions Asked from Definite Integration (Numerical)
Number in Brackets after Paper Indicates No. of Questions
JEE Advanced 2024 Paper 2 Online (2)
JEE Advanced 2023 Paper 2 Online (1)
JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2021 Paper 2 Online (3)
JEE Advanced 2020 Paper 2 Offline (1)
JEE Advanced 2019 Paper 2 Offline (1)
JEE Advanced 2019 Paper 1 Offline (1)
JEE Advanced 2018 Paper 2 Offline (1)
JEE Advanced 2016 Paper 1 Offline (1)
JEE Advanced 2015 Paper 2 Offline (1)
JEE Advanced 2015 Paper 1 Offline (1)
JEE Advanced 2014 Paper 1 Offline (1)
IIT-JEE 2010 Paper 1 Offline (1)
IIT-JEE 2009 Paper 2 Offline (1)
JEE Advanced Subjects
Physics
Mechanics
Units & MeasurementsMotionLaws of MotionWork Power & EnergyImpulse & MomentumRotational MotionProperties of MatterHeat and ThermodynamicsSimple Harmonic MotionWavesGravitation
Electricity
ElectrostaticsCurrent ElectricityCapacitorMagnetismElectromagnetic InductionAlternating CurrentElectromagnetic Waves
Optics
Modern Physics
Chemistry
Physical Chemistry
Some Basic Concepts of ChemistryStructure of AtomRedox ReactionsGaseous StateChemical EquilibriumIonic EquilibriumSolutionsThermodynamicsChemical Kinetics and Nuclear ChemistryElectrochemistrySolid StateSurface Chemistry
Inorganic Chemistry
Periodic Table & PeriodicityChemical Bonding & Molecular StructureIsolation of ElementsHydrogens-Block Elementsp-Block Elementsd and f Block ElementsCoordination CompoundsSalt Analysis
Organic Chemistry
Mathematics
Algebra
Quadratic Equation and InequalitiesSequences and SeriesMathematical Induction and Binomial TheoremMatrices and DeterminantsPermutations and CombinationsProbabilityVector Algebra3D GeometryStatisticsComplex Numbers
Trigonometry
Coordinate Geometry
Calculus