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Evaluate Integral :
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int^\infty_0 3^{-4x^2}dx = \frac{\sqrt{\pi }}{4\sqrt{log 3}}$
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Prove that $\beta(m,m)=2^{1-2m}\,\beta\left(m,\frac{1}{2}\right)(L)$
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Prove that $\int_{0}^{\pi}\frac{\sqrt{sinx}}{(5+3cosx)^{3/2}}dx\,=\frac{(\Gamma(3/4))^2}{2\sqrt{2\pi}}\cdot(H)$
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{3}^{7}\sqrt[4]{(7-x)(x-3)}\,\,dx=\frac{2}{3} \frac{(\Gamma(1/4))^2}{\sqrt{\pi}}\cdot(M)$
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Prove that $\int_{0}^{\infty}\frac{dx}{(e^x+e^{-x})^n}\,=\frac{1}{4}\beta\left(\frac{n}{2},\frac{n}{2}\right)$ . Find $\int_{0}^{\infty}sech^8x\,dx$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Evaluate $\int_{-\pi/4}^{\pi/4}(cos\,\theta+sin\,\theta)^{\frac{1}{3}}d\theta$ in terms of gamma function.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Evaluate $\int_{0}^{3}\frac{x^{3/2}}{\sqrt{3-x}}dx\,\int_{0}^{1}\frac{dx}{\sqrt{1-x^{1/4}}}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}cos(ax^{\frac{1}{n}})dx=\frac{\Gamma(n+1)} {a^n}COS\frac{n\pi}{2}\cdot (H)$
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}7^{-4x^2}dx=\frac{\sqrt{\pi}}{4\sqrt{log\,7}}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}\frac{x^7}{7^x}dx=\frac{7!}{(log\,7)^8}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Prove that $\int_{0}^{1}(x\, logx)^4dx=\frac{4!}{5^5}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Evaluate $\int_{0}^{1}\frac{dx}{\sqrt{x\,log(1/x)}}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}\,\sqrt{y}\,e^{-y^2}\,dy\,\int_{0}^{\infty}\frac{e^-{y^2}}{\sqrt{y}}\,dy=\frac{\pi}{2\sqrt2}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}\,\sqrt{x}\,e^{-\sqrt[3]{x}}\,dx=\frac{315}{16}\sqrt{\pi}$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using Runge-Kutta method of order four find $y(0.2)$ with $h=0.1$ . Given $\frac{dy}{dx}=\frac{1}{(x+y)},y(0)=1$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using R-K method of fourth order, solve $\frac{dy}{dx}=\frac{y^2-x^2}{y^2+x^2}$ given $y(0)=1$ at $x=0.2,0.4$.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Compute $y$ at $x=0.25$ by modified Euler's method , given $y'=2xy , y(0)=1$ .'
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Solve the equation $\frac{dy}{dx}={1-x}$ given y(0)=0 using modified Euler's method & tabulate the solution at x=0.1,0.2& 0.3 . Compare your results with exact solution.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using Euler's method find the approximate value of y where when x=1.5 in five steps taking h=0.1 given $\frac{dy}{dx}=\frac{y-x}{\sqrt{xy}}$ and y(1)=2
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using Euler's method find the approximate value of y where $\frac{dy}{dx}=\frac{y-x}{x}$ and y(1)=2 at x=2, taking h= 0.2 and compare it with exact value.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using Taylor's series expansion solve $\frac{dy}{dx}=-xy^2$ with x=0,y=2 and compare it with exact solution.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Using Taylor's series method, obtain the solution of the differential equation $\frac{dy}{dx}=3x+y^2$ with $x_0=0,\,y_0=0$ at $x=0.1$ correct to four decimal places.
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Solve $(x-1)^3\frac{d^3y}{dx^3}+2(x-1)^2\frac{d^2y}{dx^2}-4(x-1)\frac{dy}{dx}+4y=4\hspace{0.2cm}log(x-1)$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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Solve $(3x+2)^2\frac{d^2y}{dx^2}+3(3x+2)\frac{dy}{dx}-36y=3x^2+4x+1$ .
engineering mathematics updated 6.1 years ago by teamques10 ★ 70k
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