List of top Mathematics Questions on Definite Integral asked in MHT CET

Let \[ f(x)=\int_{1}^{4}\log[x]\ dx, \] where \([x]\) denotes the greatest integer function. Then the value of \(f(x)\) is:

If \(n\) is an odd natural number and \[ I_n=\int_0^1 e^x(x-1)^n\,dx \] then \( I_n+nI_{n-1} \) is equal to:

The value of $\int_{0}^{4} \sqrt{\frac{4-x}{4+x}} dx$ is:

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

The value of \( \displaystyle \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x} \, dx \) is:

Evaluate the integral \( \displaystyle \int_{0}^{\pi/2} \frac{\sin^n x}{\sin^n x + \cos^n x} \, dx \).

Evaluate the definite integral: \[ \int_{0}^{\frac{\pi}{2}} \sin^2 x \, dx \]

Evaluate the integral: \[ \int_{1}^{4}\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{e^x}}\right)dx \]

Evaluate the integral: \[ \int_{3}^{5} |x-4|\,dx \]

The value of \[ \int_{0}^{\pi} \left|\sin^{3}x\right| \, dx \] is:

Evaluate the definite integral. $$ \int_{\frac{\pi}{3}}^{\frac{2\pi}{3}} \frac{x}{1+\sin x} \, dx = $$

( \int_0^1 \log(x + 1) , dx = )

The value of ( \int_0^\pi |\sin^3 x| , dx ) is

If $f(x)$ is a function satisfying $f^{\prime}(x)=f(x)$ with $f(0)=1$ and $g(x)$ is a function that satisfies $f(x)+g(x)=x^{2}$. Then the value of the integral $\int_{0}^{1}f(x)g(x)dx$ is

If $I_n = \int_0^{\pi/4} \tan^n \theta d\theta$, then $I_{12} + I_{10}$ is equal to}

If $\int_0^{\frac{\pi}{2}} \frac{dx}{5+4\sin x} = A \tan^{-1} B$, then A + B =

$\int_0^{\pi / 4} \log (1+\tan x) \text{d}x=$

If $f(x) = |x-1| + |x-2| + |x-3|, \forall x \in [1,4]$, then $\int_1^4 f(x) dx =$

If $\int \frac{x^3}{\sqrt{1 + x^2}} \, dx = a(1 + x^2)\sqrt{1 + x^2} + b\sqrt{1 + x^2} + c$ (where $c$ is a constant of integration), then the value of $3ab$ is

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \, \csc^{\frac{4}{3}} x \, dx$ is equal to