CB.Calc.CHA-6.B: Determine the length of a curve in the plane defined by parametric functions, using a definite integral.

Determine the length of a curve in the plane defined by parametric functions, using a definite integral.

Example Problems

Consider the parametric curve:

x = \frac{1}{t + 4}

y = 2t^{5}

Which integral gives the arc length of the curve over the interval from

t = -3

to

t = 0

?

Consider the parametric curve:

x = \cos^{3}(t)

y = 7t

Which integral gives the arc length of the curve over the interval from

t = 0

to

t = \frac{\pi}{2}

?

Consider the parametric curve:

x = e^{10t}

y = t^{3}

Which integral gives the arc length of the curve over the interval from

t = a

to

t = b

?

1-on-1 AI tutoring aligned to CB.Calc.CHA-6.B. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.