Question

4.* Verify Green's Theorem in the plane for $\oint_C [(x^2 - xy^3)dx + (y^2 - 2xy)dy]$, where $C$ is a rectangle with vertices at $(-1, -2)$, $(1, -2)$, $(1, 1)$ and $(-1, 1)$. [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for $y$ in terms of $x$ for each part - you should then be able to simplify the integrals.] [10]

Name: 4.* Verify Green's Theorem in the plane for [(x^2 - xy^3)dx + (y^2 - 2xy)dy], where C is a rectangle with vertices at (-1, -2), (1, -2), (1, 1) and (-1, 1). [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for y in terms of x for each part - you should then be able to simplify the integrals.] [10]
Uploaded: 2021-12-25T09:33:55-08:00
Duration: 7 min 27 s
Channel: Shubham Sharma
Description: 4.* Verify Green's Theorem in the plane for [(x^2 - xy^3)dx + (y^2 - 2xy)dy], where C is a rectangle with vertices at (-1, -2), (1, -2), (1, 1) and (-1, 1). [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for y in terms of x for each part - you should then be able to simplify the integrals.] [10]

          4.* Verify Green's Theorem in the plane for $\oint_C [(x^2 - xy^3)dx + (y^2 - 2xy)dy]$, where $C$ is a rectangle with vertices at $(-1, -2)$, $(1, -2)$, $(1, 1)$ and $(-1, 1)$. [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for $y$ in terms of $x$ for each part - you should then be able to simplify the integrals.] [10]

4.* Verify Green's Theorem in the plane for [(x^2 - xy^3)dx + (y^2 - 2xy)dy], where C is a rectangle with vertices at (-1, -2), (1, -2), (1, 1) and (-1, 1). [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for y in terms of x for each part - you should then be able to simplify the integrals.] [10]

Added by Douglas W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shubham Sharma

12/25/2021

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4.* , Verify Green's Theorem in the plane for oint_C [(x^(2)-xy^(3))dx+(y^(2)-2xy)dy], where C is a rectangle with vertices at (-1,-2),(1,-2),(1,1) and (-1,1). [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for y in terms of x for each part - you should then be able to simplify the integrals.] 10 4.* Verify Green's Theorem in the plane for [(x2 -- xy3)dx +(y2 - 2xy)dy], where C is a rectangle with vertices at (1, 2), (1, -2), (1, 1) and (1, 1). [Hint: start by separating the integral into four parts, one for each side of the rectangle, and writing down an expression for y in terms of x for each part - you should then be able to simplify the integrals.] [10]