If 'V' is the region bounded by the planes x = 0, x = 2, y = 0, z = 0 and z+y = 1 then the value of the integral ([[y dx dy dz is

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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Q: Evaluate the triple integral. 3xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Graph the region of integration and evaluate the integral S, (→+x² ) dA {(x,y)|1<x² +y² < 4 and 0 <…

A: • The region R has circular symmetry, so we will use polar coordinates to evaluate this double…

Q: Use an iterated integral to find the area of the region. dy dx = y 8 7 5 4 3 2 1 -1 1 4 -1l 3. 2.

A: We need to setup and evaluate integral.

Q: Use the substititutions и — у — х, and v 3 y + 2x to evaluate the integral - (2х + у) (х — у) dx dy…

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Q: Evaluate the triple integral. 2xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

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Q: Calculate the integral/ / (x + y)² sin² (x – y) dA, where D is the region given by D = {(x, y) :…

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Q: ON Verify Green's Theorem by evaluating both integrals 7y dx + 7x*dy = J J]a дм ƏA for the path ду…

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Q: Evaluate the double integral / (3x + 2) dA I D when D is the bounded region enclosed by y = x and y…

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Q: Evaluate the double integral + y? )dædy, where N is a bounded region between y = x² and y = x³.

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Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: Verify Green's Theorem by evaluating both integrals dA dx + x2 dy ax for the given path. C: boundary…

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Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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Q: Calculate the integral/ / (x + y)* sin° (x – y) dA, where D is the region given by D = {(x, y) : |+…

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Q: Verify Green's Theorem by evaluating both integrals aM dA ƏN | y? dx + x2 dy = ду, дх for the given…

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Q: The result of the following integral ydx+x*dy where C is the region enclosed between the graphs y =x…

A: The given integral is  ∫Cxydx+x2dy where C is the region enclosed by y=x4 and y=x2

Q: Evaluate the triple integral. 3xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Compute the integral ∫∫D xy dA where D is the region bounded by y = √x, y = 6−x, y = 1.

A: Consider the given function, y=x,y=6-x and y=1 Put both the function equal to find the limit.

Q: Consider the region bounded by the curve x = y(2 - y)(3y + 1) and the y-axis shown below. I= y(2 –…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy = dA ду ax for the given path. C:…

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Q: Verify Green's Theorem by evaluating both integrals ƏN dA y? dx + x² dy = ay for the given path. C:…

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Q: Evaluate the triple integral ∭E(x+2y)dV where E is bounded by the parabolic cylinder y=2x2 and the…

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Q: The double integral of the function f(x,y) = over the region in the first quadrant y A 3, 2x bounded…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

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Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: Evaluate the triple integral. 7xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Evaluate the triple integral ∭E (x+7y)dV where E is bounded by the parabolic cylinder y=2x^2 and the…

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Q: Evaluate the double integral S, x dx dy where the region R is bounded by: 9 y = 4x – 3, 1 +x. 4 у %3…

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Q: Suppose that f(x, y) = 8x + 4y and the region D is given by {(x, y) | –1< x < 1, – 1 <y< 1}. D Then…

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Q: Evaluate || Vx2 +y? dx dy over the region R in the xy plane bounded by x² +y² = 36 - R

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Q: Verify Green's Theorem by evaluating both integrals dA v? dx + x2 dy ax for the given path. C:…

A: We have to verify the green's theorem

Q: Evaluate the double integral 4 = SS R y2 dædy over the region R={(x,y)|0 < x < 4, 1 < y < 4 }

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Q: Set-up the integral to calculate the area of a region bounded by х-у-3 and y-x2 -6x+9? A dy dx x2—…

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Q: Use Green's theorem to evaluate the integral for S[(6y-e*) dx +(8x+ lIn(4y)) dy]. where C is the…

A: Evaluate the integral              ∫C6y-e3xdx+8x+ln(4y)dy using Green's theorem, where C is the…

Q: The value of the double integral // (2x²y + 9y') d A, D where D is the region bounded by x and y = 2…

A: Given problem:-

Q: Use an iterated integral to find the area of the region. dy dx = y 6 5 4 3 2 1F -1 1 2 4

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Evaluate the 2d integral Sla ydædy, where the region 2 is defined N:= {(x, y) E R² : 0 < x < 7, sin…

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Q: Evaluate the triple integral, (2x + z) dV where E is the region bounded inside the cylinder a – y"…

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Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Express the area of the region bounded by the given line and parabola as an iterated double…

A: The equation of the line and the parabola are: C1: y = x2…

Q: Evaluate the triple integral. 5xy dV, where E is bounded by the parabolic cylinders y = x² and x =…

A: The point of intersection of the cylinder x=y2 and y=x2 is 0 and 1.

Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

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Q: Consider the region bounded by the curve a = y(2 - y)(3y2 + 1) and the y-axis shown below. y…

A: topic- application of integration

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Suppose that f(x, y) and the region D is given by {(x, y) |1< x < 2, 2 < y < 4}. Then the double…

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Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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Q: A region is bounded by the y=x2 and y=6x-x², Which of the following integrals would approximate the…

A: Option (a)

Q: (d) If R is the region bounded by y = x² and y = 2x² – 4, then | S(x, y) dA as R an iterated…

A: Given, y=x2y=2x2-4

Q: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

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