definite integral

Consider a non-negative function $f(x)$ which is continuous and bounded over the interval [2, 8]. Let $M$ and $m$ denote, respectively, the maximum and the minimum values of $f(x)$...

The integral $$\int\limits_0^1 {{{dx} \over {\sqrt {\left( {1 - x} \right)} }}} $$ is equal ________.

Consider the function $$g\left( t \right) = {e^{ - t}}\,\sin \left( {2\pi t} \right)u\left( t \right)$$ ,where $$u(t)$$ is the unit step function. The area under $$g(t)$$ is ______...

The value of the integral $$\int_{ - \infty }^\infty {12\,\,\cos \left( {2\pi t} \right){{\sin \left( {4\pi t} \right)} \over {4\pi t}}} dt\,\,$$ is __________.

The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\sc...

The value of the integral $$\,I = {1 \over {\sqrt {2\,\,\pi } }}\int\limits_0^\infty {\exp \left( { - {{{x^2}} \over 8}} \right)dx} $$ is