Explain why, for a parametric curve that is continuous on and differentiable on…

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

Explain why, for a parametric curve that is continuous on

[a,c]

and differentiable on

(a,c)

except possibly at a single point

b\,(a<b<c)

, the length of the curve from

t=a

t=c

equals the sum of the lengths computed over

[a,b]

and

[b,c]