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Multivariable Calculus

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Difficult

Particle Traveling Along an Ellipse

MVCALC-3NV6KX

A particle is traveling along an ellipse whose equation is:

$$x^2-2x+4y^2+24y+33=0$$

Which of the given formulas will compute the distance traveled from the point $(3.-3)$ to the point $(1,-4)$, if the point is traveling counterclockwise?

A

$\int^{\pi/2}_0 \sqrt{\sin^\theta+1}\,d\theta$

B

$\int^{3\pi/2}_0\sqrt{3\sin^2\theta+1}\,d\theta$

C

$\int^{3\pi/2}_0\sqrt{3\cos^2\theta+1}\,d\theta$

D

$\int^{\pi/2}_0 \sqrt{\cos^\theta+1}\,d\theta$

E

$\int^{\pi/2}_0\sqrt{3\cos^2\theta+1}\,d\theta$