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Arc Length for Parametric Curves
Grade Level
Calculus I
CAL1.146 Arc Length for Parametric Curves
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Which option correctly starts and evaluates the arc length of the parametric curve x(t)=t sin(t) + cos(t), y(t)=-t cos(t) + sin(t), 0 <= t <= 3?
A
int_0
3
sqrt((t sin(t) + cos(t))
2
+ (-t cos(t) + sin(t))
2
) dt; use the position components directly
B
int_0
3
(abs(t cos(t)) + abs(t sin(t))) dt; add the component rates
C
int_0
3
t dt; use product rule and integrate exactly
D
int_0
3
((t cos(t))
2
+ (t sin(t))
2
) dt; integrate squared speed without the square root
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