Definite Integral

The integral $\frac{1}{\pi} \int_0^{\infty} \frac{x^{2026}}{(1 + x^{2026})(1 + x^2)} dx$ evaluates to _______ (Round off to two decimal places)

In the following differential equation, the numerically obtained value of $$y(t)$$, at $$t=1$$ is ___________ (Round off to 2 decimal places). $${{dy} \over {dt}} = {{{e^{ - \alpha...

The value of the integral $$\,\,2\int_{ - \infty }^\infty {\left( {{{\sin \,2\pi t} \over {\pi t}}} \right)} dt\,\,$$ is equal to

The value of the quantity, where $$P = \int\limits_0^1 {x{e^x}\,dx\,\,\,} $$ is

The integral $$\,\,{1 \over {2\pi }}\int\limits_0^{2\Pi } {Sin\left( {t - \tau } \right)\cos \tau \,d\tau \,\,\,} $$ equals

The expression $$V = \int\limits_0^H {\pi {R^2}{{\left( {1 - {h \over H}} \right)}^2}dh\,\,\,} $$ for the volume of a cone is equal to _________.

If $$S = \int\limits_1^\infty {{x^{ - 3}}dx} $$ then $$S$$ has the value

The area enclosed between the parabola $$y = {x^2}$$ and the straight line $$y=x$$ is _______.

The volume generated by revolving the area bounded by the parabola $${y^2} = 8x$$ and the line $$x=2$$ about $$y$$-axis is