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choli [55]
3 years ago
5

Suppose F⃗ (x,y)=⟨ex,ey⟩F→(x,y)=⟨ex,ey⟩ and CC is the portion of the ellipse centered at the origin from the point (0,1)(0,1) to

the point (7,0)(7,0) centered at the origin oriented clockwise. (a) Find a vector parametric equation r⃗ (t)r→(t) for the portion of the ellipse described above for 0≤t≤π/20≤t≤π/2.
Mathematics
1 answer:
Rudik [331]3 years ago
7 0

Probably the intended ellipse is the one with equation

\dfrac{x^2}{49}+y^2=1

We can parameterize C as a piece of this curve by

\vec r(t)=\langle7\sin t,\cos t\rangle

with 0\le t\le\frac\pi2. Then

\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^{\pi/2}\langle e^{7\sin t},e^{\cos t}\rangle\cdot\langle7\cos t,-\sin t\rangle\,\mathrm dt

etc

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