- #1
mmh37
- 59
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I have been working on the following line integral:
[tex] \int_{T}^- {(-x^2y)dx + (y^2x)dy}[/tex]
where T is the closed curve consisting of the semi-circle x^2 + y^2 = a^2 (y>0) and the segment (-a,a)
I will tackle this in two steps:
1)
solve x^2 + y^2 = a^2 (y>0) for y and substitute into Integral
this gives [tex] \int_{-a}^a {- x^2 * root (a^2-x^2) }dx[/tex]
2) integrating along the x-axis - gives zero.
My problem: How can one solve the above integral in part 1? Help is much appreciated!
[tex] \int_{T}^- {(-x^2y)dx + (y^2x)dy}[/tex]
where T is the closed curve consisting of the semi-circle x^2 + y^2 = a^2 (y>0) and the segment (-a,a)
I will tackle this in two steps:
1)
solve x^2 + y^2 = a^2 (y>0) for y and substitute into Integral
this gives [tex] \int_{-a}^a {- x^2 * root (a^2-x^2) }dx[/tex]
2) integrating along the x-axis - gives zero.
My problem: How can one solve the above integral in part 1? Help is much appreciated!
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