Compute the following integrals: (a) * 2 COS E dr dy. (b) Evaluate the double integral [lnele v)/(z1v)dA where D is the triangle with vertices (0, 0), (1,0) and (0, 1). (c) Compute the volume of the ellipsoid bounded by the surface r + y + z2 - 1, a > 0.

Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the net flux through…

A: consider the equation

Q: Figure 2 illustrates a lamina R, which is bounded by y =x and y=/x. 2- R Figure 2 i) By using double…

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Q: Evaluate the surface integral JSF dS where F = (5x, 3z, -3y) and S is the part of the sphere a² +…

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Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

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Q: | Calculate the surface integral /| G(r) dA, where G = (12 the parametrization r(u, v) = [3u, 2v,…

A: Introduction: We know that the formula for the surface integral is given by,…

Q: Find the volume of the solid bounded from above by the surface z = (64 − 4x^2 − 9y^2)^(1/3) and from…

A: To find - Find the volume of the solid bounded from above by the surface z = 64 - 4x2 - 9y213 and…

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: Use double integral in polar coordinates to find the area of the portion of the paraboloid 2z=x² +y²…

A: Given that 2z=x2+y2 that lies in x2+y2=4 The aim is to find the area.

Q: FIND THE CENTROID OF THE AREA BOUNDED BY THE CURVE r= a (1 + sin e).

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Q: 2. Find the centroid of the region R = {(x,y): x ≥ y²/2, x ≤ y}.

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Q: Let R be the region that is below y=√x between x= 1 and x= 4. (a) Find the centroid of this region.…

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Q: Answer the following questions about the given integral: II.(x+ y)e*- dA , where R is a region…

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Q: Q6) (a) Determine the integral ſ dxdy over the surface S of the upper hemiellipsoid 2+2=1 1. (b)…

A: Given That : The equation of hemiellipsoid is: x2a2+y2b2+z2c2=1 To Find : a)∫∫sdxdy b) Volume of the…

Q: Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R. a = 2 b…

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Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

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