Evaluate the definite integral $\int_0^3 [x] \, dx$,where $[x]$ denotes the greatest integer function.

$\int_{-1}^1 \frac{\cosh x}{1+e^{2 x}} d x$ is equal to :

Consider the matrices $A = \begin{bmatrix} 2 & -5 \\ 3 & m \end{bmatrix}$,$B = \begin{bmatrix} 20 \\ m \end{bmatrix}$,and $X = \begin{bmatrix} x \\ y \end{bmatrix}$. Let the set of all $m$,for which the system of equations $AX = B$ has a negative solution (i.e.,$x < 0$ and $y < 0$),be the interval $(a, b)$. Then $8 \int_a^b |A| dm$ is equal to.............

The value of $\int_{0}^{4} \{ \sqrt{x} \} dx$,where $\{ \}$ denotes the fractional part of $x$,is

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

Evaluate the definite integral $\int_{0}^{2} \frac{6 x+3}{x^{2}+4} d x$.