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959
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Compute the value of
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1
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2.1k
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Find the mass of a lamina in the form of an eclipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} - 1$, if the density at any point varies as the product of the distance from the azes of the ellipse.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the perimeter of the curve $r = a (1- cos\theta$)
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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870
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Given $\int^x_0 \frac{dx}{x^2 + a^2} = \frac{1}{a} tan^-1 (\frac{x}{a})$, using DUIS find the value of $\int^x_0 \frac{dx}{(x^2 + a^2)^2}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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1.1k
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Compute the value of
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Prove for an asteroid $x ^{2/3} + y ^{2/3} = a^{2/3}$, the line $\theta = \frac{\pi }{6}$ divide the arc in the first quadrant in a ratio 1:3
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the mass of the leminiscate $r^2 = a^2 cos 2\theta$ if the density at any point is proportional to the square of the distance from the pole.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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830
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Using DUIS prove that $\int^{\infty}_0 e^{-(x^2+\frac{a^2}{x^2})}dx=\frac{\sqrt\pi}{2} e^{-2a}, a \gt 0$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the length of the cycloid from one cusp to the next where
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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3.5k
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Show that the perimeter of the lemiscate $r^2=a^2\, cos2\theta$ is $\frac{a}{\sqrt{2\pi}}\left[1/4\right]^2$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that the whole perimeter of the cardioide $r=a(1+cos\theta)$ is $8a$. Also prove that the arc of the upper half of the cardioide is bisected at $\theta = \frac{\pi}{3}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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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 6.0 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 6.0 years ago by teamques10 ★ 70k
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1
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4.3k
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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 6.0 years ago by teamques10 ★ 70k
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1
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8.9k
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Find the length of the loop of the curve $9y^2=(x+7)(x+4)^2 $
engineering mathematics updated 6.0 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 6.0 years ago by teamques10 ★ 70k
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1.5k
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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 6.0 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 6.0 years ago by teamques10 ★ 70k
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1.2k
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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 6.0 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 6.0 years ago by teamques10 ★ 70k
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Evaluate $\int^{\infty}_0 \frac{e^{-x^3}}{\sqrt x} \ dx$
engineering mathematics updated 6.0 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 6.0 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 6.0 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 6.0 years ago by teamques10 ★ 70k
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933
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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 6.0 years ago by teamques10 ★ 70k
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