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919
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If Y satisfies the equation $\frac{dy}{dx} = x^2 y -1$ with $x_0 = 0, y_0 = 1$, using Taylors series method find y at x = 0.1 (take h = 0.1)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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910
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Show that $\int^1_0 \frac{x-1}{log x} dx = log (a+1)$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Evaluate the :
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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801
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Solve $\frac{dy}{dx} = xy$ with the help of Eulers method, given that y(0) = 1 and find y when x = 0.3 (h = 0.1)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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863
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Show that :
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using modified Eulers method, find an appropriate value of y at x = 0.2 in two step taking h = 0.1 and using iteration, given that $\frac{dy}{dx} = x + 3y, y = 1 \ when \ x = 0.$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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934
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Use Taylors series method to find a solution of $\frac{dy}{dx} = 1 + y^2, y(0) = 0$ at x = 0.1 taking h = 0.1 correct to three decimal value.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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794
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Evaluate $\int^\infty_0 \frac {e^{-x^2}}{\sqrt x} \ dx$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using Beta function evaluate $\int^{\frac{\pi}{6}}_0 cos^6 3\theta \ sin^2 6 \theta \ d\theta$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Use Taylors series method to find a solution of $\frac{dy}{dx} = 1 + x y, \ y (0) = 0 for \ x = 0.2$ taking h = 0.1 correct to four decimal places
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Apply Runge Kutta method of fourth order to find an appropriate value of y when x = 0.4 given that $\frac{dy}{dx} = \frac{y-x}{y+x}, \ y = 1$ when x = 0 taking h = 0.2
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1.0k
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Evaluate Integral :
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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4.5k
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Show that $\int^\infty_0 3^{-4x^2}dx = \frac{\sqrt{\pi }}{4\sqrt{log 3}}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
1
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1
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16k
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Prove that $\beta(m,m)=2^{1-2m}\,\beta\left(m,\frac{1}{2}\right)(L)$
engineering mathematics updated 6.0 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 6.0 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 6.0 years ago by teamques10 ★ 70k
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995
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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 6.0 years ago by teamques10 ★ 70k
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1.5k
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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 6.0 years ago by teamques10 ★ 70k
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1.2k
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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 6.0 years ago by teamques10 ★ 70k
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1
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1.1k
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1
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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 6.0 years ago by teamques10 ★ 70k
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1.3k
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Show that $\int_{0}^{\infty}7^{-4x^2}dx=\frac{\sqrt{\pi}}{4\sqrt{log\,7}}$ .
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1.2k
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Show that $\int_{0}^{\infty}\frac{x^7}{7^x}dx=\frac{7!}{(log\,7)^8}$ .
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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3.0k
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Prove that $\int_{0}^{1}(x\, logx)^4dx=\frac{4!}{5^5}$ .
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1.0k
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Evaluate $\int_{0}^{1}\frac{dx}{\sqrt{x\,log(1/x)}}$ .
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1.7k
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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 6.0 years ago by teamques10 ★ 70k
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