The value of $\int_{-1}^{2} \frac{|x|}{x} d x$ is

If $b > a$,then $\int_a^b \frac{dx}{\sqrt{(x-a)(b-x)}}$ is equal to

$\int_0^{b - c} f''(x + a) \, dx = $

Let $[t]$ denote the greatest integer function. If $\int_0^{2.4} [x^2] dx = \alpha + \beta \sqrt{2} + \gamma \sqrt{3} + \delta \sqrt{5}$,then $\alpha + \beta + \gamma + \delta$ is equal to $..............$.

Let $f:[0,1] \rightarrow [0, \infty)$ be a continuous function such that $\int_0^1 f(x) dx = 10$. Which of the following statements is $NOT$ necessarily true?

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