The positive value of $x$ satisfying the equation $\int_x^1(1-t) dt = \frac{1}{2}$ is

If $[.]$ represents the greatest integer function,then evaluate the integral: $\int_{\frac{3 \pi}{4}}^\pi \left[ \sin x + \left[ \frac{4 x}{\pi} \right] \right] dx$.

$\int_0^{x} \frac{t^2}{\sqrt{a^2+t^2}} dt =$

The greatest value of the function $F(x) = \int_1^x {|t| \, dt}$ on the interval $\left[ -\frac{1}{2}, \frac{1}{2} \right]$ is:

If $f$ is integrable on $[0, a]$,then the function $h$ defined on $[0, a]$ as $h(x) = \int_0^x f(t) dt$ is integrable on $[0, a]$. Which of the following functions is also integrable on $[0, a]$?

Let $a, b, c$ be non-zero real numbers such that $\int_0^3 {(3ax^2 + 2bx + c)\,dx} = \int_1^3 {(3ax^2 + 2bx + c)\,dx}$,then