- #1

Tom McCurdy

- 1,020

- 1

The problem:

Evaluate the integral

[tex] \oint_{c} Fdr [/tex] for [tex] F = (2xy^4)i+(2x^2y^3)j [/tex] on the curve C consisting of the x-axis from x=0 to x=1, the parabola y=1-x^2 up to the y-axis, and the y-axis down to the origin

Here is what I triedF(x,y)=[tex]<2xy^4,2x^2y^3> [/tex][tex] \int\int_{D} =[(2x^2y^3)*\frac{\partial}{\partial x}-(2xy^4)\frac{\partial}{\partial y}] dA [/tex]= [tex] \int_{0}^{1} \int_{1-x^2}^{0} [4xy^3-8xy^3] dy dx [/tex]=1/10

Evaluate the integral

[tex] \oint_{c} Fdr [/tex] for [tex] F = (2xy^4)i+(2x^2y^3)j [/tex] on the curve C consisting of the x-axis from x=0 to x=1, the parabola y=1-x^2 up to the y-axis, and the y-axis down to the origin

Here is what I triedF(x,y)=[tex]<2xy^4,2x^2y^3> [/tex][tex] \int\int_{D} =[(2x^2y^3)*\frac{\partial}{\partial x}-(2xy^4)\frac{\partial}{\partial y}] dA [/tex]= [tex] \int_{0}^{1} \int_{1-x^2}^{0} [4xy^3-8xy^3] dy dx [/tex]=1/10

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