Zela101
  • Zela101
Evaluate Integral F*dr along the curve C
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Zela101
  • Zela101
\(\large F(x,y)=x^2i+xyj\) \(\large C:r(t)=2costi+2sintj;~~(0\le t\le\pi)\)
ganeshie8
  • ganeshie8
|dw:1449857927702:dw|
Zela101
  • Zela101
x=2cost y=2sint?

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Zela101
  • Zela101
WAIT I GOT IT NOW lol
ganeshie8
  • ganeshie8
yeah you may use that parameterization
Zela101
  • Zela101
(\(2cost)^2i+(2cost)^2(2sint)^2j\)
Zela101
  • Zela101
\(F•dr=(2cost)^2i+(2cost)^2(2sint)^2j)•(2costi+2sintj)\)
ganeshie8
  • ganeshie8
\(\large F(x,y)=x^2i+xyj\) right ?
Zela101
  • Zela101
\(F•dr=(2cost)^2i+(2cost)(2sint)j)•(2costi+2sintj)\)
ganeshie8
  • ganeshie8
why are you squaring the j component
Zela101
  • Zela101
Yes my bad
Zela101
  • Zela101
Thanks @ganeshie8 :)
ganeshie8
  • ganeshie8
don't forget to plugin the differentials
ganeshie8
  • ganeshie8
dr = (dx, dy) = (x', y')dt
ganeshie8
  • ganeshie8
\(F•dr=((2cost)^2i+(2cost)(2sint)j)•(2costi+2sintj)^{\color{Red}{'}}\)
Zela101
  • Zela101
\[ \int\limits_{C}^{} F(r(t))•r'(t) dt \]
Zela101
  • Zela101
\(\int\limits_{0}^{\pi}-8cos^2tsint+8cos^2tsint ~ dt\) \(\int\limits_{0}^{\pi}0~ dt=0\) which means vector field F is normal to C at every point.

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