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Evaluate $\int_{0}^{1}\int_{0}^{\sqrt{1-y^2}}\frac{cos^{-1}x}{\sqrt{1-x^2}\,\sqrt{1-x^2-y^2}}dx\,dy$ by changing the order of integration.
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Change the order of the integration in the following $\int_{0}^{1/2}\int_{0}^{\sqrt{1-4y^2}}\frac{(1+x^2)}{\sqrt{1-x^2}\,\sqrt{1-x^2-y^2}}dx\,dy$ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\iint r^3\, drd\theta$ over the area included between the circles $r=2sin\theta$ and $r=2cos\theta$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\iint_R y\,dxdy$ where 'R' is the region bounded by $y^2=4x$ & $x^2=4y$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\iint_R\frac{2xy^5}{\sqrt{1+x^2y^2-y^4}}dxdy$ where 'R' is the region of the triangle whose vertices are $(0,0),\, (1,1),\,(0,1)$ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\iint(x^2+y^2)dxdy$ over the area enclosed by the curve $y=4x,\,x+y=3,\,y=0,\,y=2$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int_{0}^{1}\int_{0}^{\sqrt{1+x^2}}\frac{dy\,dx}{(1+x^2+y^2)}$ .
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the length of the curve $x = \frac{y^3}{3} + \frac{1}{4y}$ from y = 1 to y = 2
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the mass of the lamina bounded by the curves
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Evaluate $\int^6_0 \frac{dx}{1+3x}$ by using i) Trapezoidal ii) Simpsons $(1/3)^{rd}$ and iii) Simpsons $(3/8)^{th}$ rule
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the value of the integral $\int^1_0 \frac{x^2}{1 +x^2} dx$ using (i) Trapezoidal rule (ii) Simpsons $1/3^{rd}$ rule (iii) Simpsons $3/8^{th}$ rule
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Show that the length of the curve $9ay^2 = x(x-3a)^2$ is $4\sqrt3a$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Apply Runge-kutta Method of fourth order to find an approximate value of y when x = 0.2 given that $\frac{dy}{dx} = x + y$ when y = 1 at x = 0 with step size h = 0.2
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Find the area inside the circle $r = a sin \theta$ and outside the cardioide $r = a (1 + cos \theta)$
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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Compute the value of
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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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 6.2 years ago by teamques10 ★ 70k
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Find the perimeter of the curve $r = a (1- cos\theta$)
engineering mathematics updated 6.2 years ago by teamques10 ★ 70k
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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 6.2 years ago by teamques10 ★ 70k
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Compute the value of
engineering mathematics updated 6.2 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 6.2 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 6.2 years ago by teamques10 ★ 70k
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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 6.2 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 6.2 years ago by teamques10 ★ 70k
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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 6.2 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 6.2 years ago by teamques10 ★ 70k
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