The value of continuous |DEFINITE INTEGRATION|JEE MAIN 2026

Competishun Header

JEE MAIN 2026

08-04-2026_S2

Question

Let $f(x)=\left\{\begin{array}{cc}\frac{1}{3} & , x \leq \pi / 2 \\ \frac{\mathrm{~b}(1-\sin x)}{(\pi-2 x)^2} & , x>\pi / 2\end{array}\right.$. If $f$ is continuous at $x=\pi / 2$, then the value of $\int_0^{3 \mathrm{~b}-6}\left|x^2+2 x-3\right| \mathrm{d} x$ is :

Select the correct option:

A

5

B

2

C

3

D

4

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

Start Preparing for JEE with Competishun

Filters 0

Showing 18 questions

Q JEE MAIN 20262026

Given below are two statements
Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .
Statement II:...

JEE MainChemistryMedium

View Solution→

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text {rd }}$ of its initial volume $\left(V_0=3\right.$ litre $)$ by applying required...

JEE MainPhysicsEasy

View Solution→

An ideal gas undergoes a process maintaining relation between pressure ( $P$ ) and volume ( $V$ ) as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$,...

JEE MainPhysicsMedium

View Solution→

In a Young double slit experiment, the wavelength of incident light is 6000 A , the separation between slits $S_1$...

JEE MainPhysicsEasy

View Solution→

Arrange the following resultant mixtures in increasing order of their pH values A. $10 \mathrm{~mL} 0.2 \mathrm{MCa}(\mathrm{OH})_2+25 \mathrm{~mL} 0.1 \mathrm{MHCl}$...

JEE MainChemistryMedium

View Solution→

Solid carbon, CaO and $\mathrm{CaCO}_3$ are mixed and allowed to attain equilibrium at TK . $$ \begin{aligned} & \mathrm{CaCO}_3(\mathrm{~s}) \mathrm{f}...

JEE MainChemistryEasy

View Solution→

Consider the reaction
$$ 2 \mathrm{H}_2 \mathrm{~S}(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{l})+2 \mathrm{SO}_2(\mathrm{~g}) $$
The magnitude of enthalpy change...

JEE MainChemistryMedium

View Solution→

Consider two radiations of wavelengths

JEE MainChemistryEasy

View Solution→

' $x$ ' is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride...

JEE MainChemistryHard

View Solution→

QJEE MAIN 20262026

Decomposition of a hydrocarbon follows the equation $\mathrm{k}=\left(5.5 \times 10^{11} \mathrm{~s}^{-1}\right) \mathrm{e}^{\frac{-28000 \mathrm{~K}}{\mathrm{~T}}}$. The activation energy of reaction is $\_\_\_\_$...

JEE MainChemistryMedium

View Solution→

QJEE MAIN 20262026

In a closed flask at 600 K , one mole of $\mathrm{X}_2 \mathrm{Y}_4(\mathrm{~g})$ attains equilibrium as given below :
$...

JEE MainPhysicsEasy

View Solution→

Number of paramagnetic complexes among the following is $\_\_\_\_$ .

JEE MainChemistryMedium

View Solution→

QJEE MAIN 20262026

500 mL of $0.2 \mathrm{M} \mathrm{MnO}_4^{-}$solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises...

JEE MainChemistryMedium

View Solution→

QJEE MAIN 20262026

An alkane $(Y)$ requires 8 moles of oxygen for complete combustion and on chlorination with $\mathrm{Cl}_2 / \mathrm{h} \nu,(\mathrm{Y})$ gives...

JEE MainChemistryMedium

View Solution→

Q JEE MAIN 20262026

An excess of $\mathrm{AgNO}_3$ is added to 100 mL of a 0.05 M solution of tetraaquadichloridochromium (III) chloride. The number...

JEE MainChemistryEasy

View Solution→

QJEE MAIN 20262026

Treatment of a gas ' $X$ ' with a freshly prepared ferrous sulphate solution gives a compound ' $Y$ '...

JEE MainChemistryEasy

View Solution→

Consider the reaction $\mathrm{Xf} \quad \mathrm{Y}$ at 300 K . If $\Delta \mathrm{H}^0$ and K are $28.40 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and...

JEE MainChemistryMedium

View Solution→

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1 / 2}=3$ hour. The...

JEE MainChemistryMedium

View Solution→