Evaluate the integral f*dr where f(x,y)=<-y,x^2> and c consists of te arc of the parabola y=2x^2 from (-1,2) to (1,2)

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20-10-2017
Mathematics

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Evaluate the integral f*dr where f(x,y)=<-y,x^2> and c consists of te arc of the parabola y=2x^2 from (-1,2) to (1,2)

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LammettHash LammettHash · Answer 1 · 2017-10-20T22:31:43+02:00

LammettHash LammettHash

20-10-2017

[tex]y=2x^2\implies\mathbf r(x)=\langle x,2x^2\rangle[/tex]

[tex]\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_{t=-1}^{t=1}\langle-2x^2,x^2\rangle\cdot\langle1,4x\rangle\,\mathrm dx[/tex]
[tex]=\displaystyle\int_{-1}^1(8x^3-2x^2)\,\mathrm dx[/tex]
[tex]=-\dfrac43[/tex]

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