Sketch the region R and evaluate the iterated integral f(x, у) dA. с 30 *15 (х + у) dx dy ly/2 16 30 14 25 12 20 10 y 8 У 15 6 10 4- 5- 2 10 15 20 25 30 2 4 6 10 12 14 16 16 30 14 25 12 20 10 y 8 У 15 6 10 4 5- 2- 10 15 20 25 30 2 4 8. 10 12 14 16 f(x, у) dA %3D

Q: The figure below shows the expression for the x-centroid of line L. Suppose length L is 10 cm and…

A: Suppose L is the length of the line. Then, the x-coordinate of the centroid of the line is…

Q: Let F =   Find the outer flux of F through the surface S that is the portion of the paraboloid z =…

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Q: For F(x, y, z) = x²z² i+ sinx z²j+zx²y*k, find div F and curl F.

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

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Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Evaluate the line integral, where C is the given space curve. [xerza xez ds, C is the line segment…

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Q: ·볼+1 2x - y dx dy, Use the transformation to evaluate 2x-y where u = v = % and integrating over an…

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Q: Which of the following integral is the integral f f, el+s)/(c~-3) dA where Ris the trapezoidal…

A: To   sketch the region R   and choose an appropriate change of variables          for the…

Q: sy2-3x²+9 J. Tra St 2 Convert x - gy dzdydx to integral of cyclındri cal coordinatcs then evaluate

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Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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Q: State the area of the region, determined by the lines, y = 13z, y = 2z + 2, y = 13z – 4, y = 2x + 7…

A: we will use transformation and jacobian here.

Q: Find the centroid (ã, j) of the region bounded by: y = 8x? + 5x, y= 0, x = 0, and x = 1 6. x= y =

A: Given equations,  y=8x2 + 5x, y = 0, x =0 and x =1. First of all let us find area of the region…

Q: Given the line integral | (2x2° + 6y) da + (6x – 2yz) dy + (3a² z² – y²) dz. Let C be the path that…

A: Note that the following integral reduces like this :

Q: Calculate SS dxdy D (x+y)² in Surface D limited to curve y=x² and the lines 2 Y=x+2 and x = 1.

A: Given:  integral ∫∫Ddxdy(x+y)2  in the surface D limited to curve y=x2 , y=x+2, x=1  To Find : value…

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: 1/(u + v), y (-u + v) 13. Use the change of variables (planar transformation) x = to evaluate ff(x +…

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Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: + 1 -оу-х -oy=x2

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Q: noose an appropriate change of variables to c al over a rectangle in the uv-plane.

A: Introduction:   The definite integral can be applied to multiple-variable functions. Consider the…