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wlad13 [49]
3 years ago
5

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)

Mathematics
1 answer:
d1i1m1o1n [39]3 years ago
3 0
y=2x^2\implies\mathbf r(x)=\langle x,2x^2\rangle

\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
=\displaystyle\int_{-1}^1(8x^3-2x^2)\,\mathrm dx
=-\dfrac43
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