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Show that the length of one arc of the cycloid $x=a(\theta-sin\theta)$ and $y=a(1-cos\theta)$ is $8a$ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the total length of the arc of the $x^{2/3}+y^{2/3}=a^{2/3} $ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find arc length of the parabola $x^2=4y $ which lies inside the circle $x^2+y^2=6y$ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the length of the loop of the curve $9y^2=(x+7)(x+4)^2 $
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int_{-1}^{1}\frac{1}{1+x^2}dx$ by using (i)Trapezoidal rule (ii) Simpon's 1/3 rule (iii) Simpson's 3/8 rule .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int_{0}^{\infty}\frac{e^{-\beta x}sin\alpha x}{x}dx $ and hence deduce $ \int_{0}^{\infty}\frac{sinx}{x}dx=\frac{{\pi}}{2}$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Show that $\int_{0}^{\infty}e^{-bx{^2}}\,cos2ax\,dx=\frac{1}{2}\sqrt{\frac{\pi}{b}}.e^{{-a}^{2}/2}\,\,,b>0\left[Assume \int_{0}^{\infty}e^{{-x}^2}dx=\frac{\sqrt{\pi}}{2}\right]$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Prove that $\int_{0}^{\infty}\frac{tan^{-1}ax}{x(1+x^2)}dx\,=\frac{\pi}{2}log(1+a)\,,\,a\geq0\,,a\neq 1 $
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Prove that $\int_{0}^{\infty}\frac{e^{-x}-e^{-ax}}{x\,secx}dx\,=\frac{1}{2}log\left(\frac{a^2+1}{2}\right)\,\,\,,\,a\geq0$ using DUIS .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int^{\infty}_0 \frac{e^{-x^3}}{\sqrt x} \ dx$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Solve $\frac{dy}{dx} = 1 + xy $ with initial condition. $x_0 = 0, y_0 = 0.2$ by Taylor's series method. Find the approximate value of y for x = 0.4 (step size 0.4)
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Show that $\int^\pi _0 \frac{log(1 + acosx)}{cosx} dx = \pi \ sin^{-1} a \ 0 \leq a \leq 1$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Solve $\frac{dy}{dx} = x^3 + y$ with initial conditions y(0) = 2 at x = 0.2 in steps of h = 0.1 by Runge Kutta method of fourth order.
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int^1_0 x^5 sin^{-1} x \ dx$ and find the value of $\beta (\frac{9}{2} , \frac{1}{2})$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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969
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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 6.2 years ago by teamques10 ★ 70k
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960
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Show that $\int^1_0 \frac{x-1}{log x} dx = log (a+1)$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate the :
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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852
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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 6.2 years ago by teamques10 ★ 70k
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Show that :
engineering mathematics updated 6.2 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 6.2 years ago by teamques10 ★ 70k
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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 6.2 years ago by teamques10 ★ 70k
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832
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Evaluate $\int^\infty_0 \frac {e^{-x^2}}{\sqrt x} \ dx$
engineering mathematics updated 6.2 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 6.2 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 6.2 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 6.2 years ago by teamques10 ★ 70k
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