integration

A square metal sheet of 4 m × 4 m is placed on the x-y plane as shown in the figure below. If the surface charge density (in µC/m²) on the sheet is ρs(x, y) = 4|y|, then the total...

Let x1(t) = u(t + 1.5) - u(t - 1.5) and x2(t) is shown in the figure below. For y(t) = x1 (t) * x2 (t), the $\int_{-\infty}^{\infty}y(t)dt$ is ________ (rounded off to the nearest...

The families of curves represented by the solution of the equation $${{dy} \over {dx}} = - {\left( {{x \over y}} \right)^n}$$ for n = –1 and n = 1 respectively, are

Taylor series expansion of $$f\left( x \right) = \int\limits_0^x {{e^{ - \left( {{{{t^2}} \over 2}} \right)}}} dt$$ around 𝑥 = 0 has the form f(x) = $${a_0} + {a_1}x + {a_2}{x^2}...

Which one of the following is the general solution of the first order differential equation $${{dy} \over {dx}} = {\left( {x + y - 1} \right)^2}$$ , where $$x,$$ $$y$$ are real ?

The variance of the random variable $$X$$ with probability density function $$\,f\left( x \right) = {1 \over 2}\left| x \right|{e^{ - \left| x \right|}}\,\,$$ is ___________.

The bilateral Laplace transform of a function $$f\left( t \right) = \left\{ {\matrix{ {1\,if\,a \le t \le b} \cr {0\,otherwise} \cr } } \right.$$ is

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

Match the application to appropriate numerical method Applications $$P1:$$ Numerical integration $$P2:$$ Solution to a transcendental equation $$P3:$$ Solution to a system of linea...

A sinsoidal signal, v(t) = A sin(t), is applied to an ideal full-wave rectifier. Show that the Laplace Transform of the output can be written in the form, $${V_0}\left( s \right) =...

The response of an initially relaxed linear constant parameter network to a unit impulse applied at $$t = 0$$ is $$4{e^{ - 2t}}u\left( t \right).$$ The response of this network to...