List of top Mathematics Questions on integral asked in JEE Main

Let $f(x)= \begin{vmatrix} 1+\sin ^2 x & \cos ^2 x & \sin 2 x \\ \sin ^2 x & 1+\cos ^2 x & \sin 2 x \\ \sin ^2 x & \cos ^2 x & 1+\sin 2 x\end{vmatrix}, x \in\left[\frac{\pi}{6}, \frac{\pi}{3}\right] $ If $\alpha$ and $\beta$ respectively are the maximum and the minimum values of $f$, then

The integral $∫^∞_0 \frac{6}{(e^{3x} + 6e^{2x} + 11e{x} + 6)}dx$

If the value of $∫_{-0.15}^{0.15} |100x^{2}-1|dx = \frac{k}{3000}$, then the value of k is?

Let $f(x)=x+\frac{a}{\pi^2-4} sinx+\frac{b}{\pi^2-4} cos x$, $x∈R$ be a function which satisfies $f(x)=x+∫_0^{\frac{\pi}{2}} sin(x+y) f(y)dy$. Then (a+b) equal to

Let [x] denote the greatest integer ≤ x. Consider the function $f(x)=max \{x^2,1+[x] \}$. Then the value of the integral $∫_0^2 f(x)dx$ is

Let $I(x)=\int\frac{x+1}{x(1+xe^x)^2} dx$, x>0. If $\lim\limits_{x\rightarrow\infin}I(x)=0$, then I(1) is equal to

Let [t] denote the greatest integer ≤t. Then $\frac{2}{π} \int\limits_{\frac{\pi}{6}}^{\frac{5\pi}{6}} (8 [cosec x]-5[cot x]) dx$is equal to ______.

Let [t] denote the greatest integer function. If $\int\limits_0^{2.4}[x^2]dx=α+β√2+γ√3+δ√5,$ then α+β+γ +δ is equal to _____.

If $\int_{0}^{1} $ 1/(5+2x-2x²)(1+e^(2-4x)) dx = 1/log_e (α+1/β) a, β>0, then a⁴- β⁴ is equal to

The value of the integral $∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}$ is equal to

If $∫\frac{1}{x}$ $√{\frac{1-x}{1+x}}$ dx = $g(x) + c,g(1) = 0$ , then g $(\frac{1}{2})$
is equal to

The integral $∫_0^ 1 \frac{ 1}{7^{[\frac{1}{z}}]}dx$ where [⋅] denotes the greatest integer function, is equal to

The odd natural number $a$, such that the area of the region bounded by $y=1, y=3, x=0$, $x=y^a$ is $\frac{364}{3}$, equal to :

The value of the integral $∫^2_{-2}\frac{ |x^3+x|}{(e^x|x|+1)}dx$ is equal to:

The integral
$\frac{24}{\pi} \int_{0}^{\sqrt{2}} \frac{2 - x^2}{(2 + x^2) \sqrt{4 + x^4}} \, dx$
is equal to _______.

The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where $ [x] $ denotes the greatest integer less than or equal to $ x $, is:

If $\int \frac{dx}{x^3 (1+x^6)^{\frac{2}{3}}} = f(x) (1+ x^{6})^{\frac{1}{3}} + C$ where C is a constant of integration, then $f(x)$ is equal to :

The integral

\int \frac{\sin^{2} x \cos^{2} x}{{(\sin^{5} x + \cos^{3} x \sin^{2} x + x \cos^{2} x + \cos^{5} x)}^{2}} d x

is equal to:

$I(x)=\int\frac{6dx}{sin^2x(1+\cot x)^2}$and I(0) then I ($\frac{\pi}{2}$) is equal to

Area bounded by y = -2|x| and y = x|x| is:

if $y=\int\frac{e^{\tan x}dx}{\cos^2x(1+e^{2\tan x})}$ and y(0)=6 then y$\frac{\pi}{4}$ is equal to