10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: 7. In AVYX, the centroid is Z. Use the diagram to solve the problems. If VP = 51, find VZ and ZP.

A: We use the property ,the centroid divides each medians in the ratio 2:1.

Q: e (2 +y+2) dV, JIIE V + y? + z? where E is the region bounded by the spheres a? + y? + 22 = 1 and r2…

A: ∭e-x2+y2+z2x2+y2+z2dv

Q: 14. Evaluate o 4y dr + 3r dy, where C is the trapezoid with vertices (0,0), (2,0), (6, 2) and (0,…

A: The solution are next step

Q: 4) The half-widths of a ship with a length of 60 m at the loaded waterline are given in the table…

A: As interval is divided into 6 equal parts . So, n=6 h=x1-x0=1-0=1 y0=f0=fx0=f0=2.85…

Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: 6. Evaluate (a + y) da dy dz, where D is the tetrahedron with vertices (0,0,0), (1,0, 0), (0, 1, 0)…

A: Introduction: The triple integral is applicable to find the volume of a solid enclosed by given…

Q: Evaluate the line integral g. xy? dx + 2x²y dy, where C is the triangle with vertices (0,0), (2, 2),…

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Q: 5. Let R be the region in the first quadrant within the circle z² + y? = 4, outside the circle (z –…

A: Region is in the first quadrant :-    Hence, region the region between these circles in above…

Q: Compute 3xy dS, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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Q: 3. Evaluate Iffa a x dV, S is the tetrahedron bounded by the S planes x+y+3z = 6, x = 0, y = 0 and 2…

A: We have the that S is bounded by the planes : x+y+3z=6x=0y=0z=0 So, from x+y+3z=6 we get z=6-x-y3…

Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Green's…

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Q: 5 + 2? + y, the cylinder Evaluate e dV where E is enclosed by the paraboloid z = E 2 + y? = 1, and…

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Q: 23 + 3 4. Evaluate the integral dz, where C is the circle (a) |z + 3| = 3, (b) |z| = 3, (c) |z| = 7.…

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Q: Use either form of Green's Theorem to evaluate the following line integral. $9x²1² 6 C $9x³y² dx +…

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Q: 4. If M is a centroid of triangle WOR and WM = 16, what is WX? %3D W Y M R

A: centroid:- i). It is the intersection point of all the medians of a triangle. ii). It divides the…

Q: Finel a formal solhon to the inital- boundary valve problem. Ugla, t) =6 uxx (x;t) , oexo ulx,0) = ,…

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Q: 7. If F = (yz,-2xz,xy), the value of ||F.n dS , where S is a sphere of radius a centered at the…

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Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Evaluate ||| Vx2 + y2 dV, where E is the region that lies inside the cylinder x2 + y? = 25 and…

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Q: 5. Use Cartesian coordinates to evaluate If y² dv where D is the tetrahedron in the first octant…

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Q: 1. Evaluate I = D xy dA, where D is the triangular region with vertices (0,0), (0, 1), and (1,1).

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 4. Evaluate ([[. (2x+3y)dxdydz where S is the tetrahedron in the first octant bounded by the…

A: The objective is to solve the integral: ∫∫∫S2x+3ydxdydzS: tetrahedron in first octant bounded by the…

Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: 3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x…

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Q: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

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Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: (3) Find The selution of the intigl ualue problem ts =y+ 3 Vy?+E, yle) =0 yl-e) 3,-2 %3D of the…

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Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: 2. Evaluate the given line integral, (-y, x – y) · dR, where C is the line segment from (2,0) to (0,…

A: Using parametric equation, line integration is evaluated.

Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: Use Green's Theorem to evaluate x dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 5. USC cyllndrical coordinates. Evaluatc (k4)dv, where E IS the solid that ies betwern the cylinders…

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Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: 3: Find the surface area of the part of the paraboloid z = and above the first quadrant. 196 - x -y…

A: The surface area of paraboloid is defined as the sum of the area of all the faces of paraboloid. it…

Q: 3.use Greens theorem s (1+x5 dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0),(1,3)…

A: Apply greens theorem

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

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Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: 2) The double integnal | 3x ekdy, whetzeT is the tniang le of VErtices 6,0),c2,0) ond (eti-2),…

A: The double integral is an integral with respect to two different variables the integral of a…