AP Calculus BC Cha 6 B Determine the Length of a Curve in the Plane Defined By Parametric Functions Using a Definite Integral Questions

Practise AP Calculus BC 9.3 by deriving parametric arc-length integrals from x'(t) and y'(t), then evaluating curve lengths over specified intervals.

Exam points

Build the arc-length integrand from dx/dt and dy/dt over the stated t-interval
Evaluate a parametric arc-length definite integral to obtain the curve's numerical length

[Maximum number: 1]

7. Given the parametric equations $x(t)=2 t^{2}-1$ and $y(t)=3+2 t^{3 / 2}$ , which expression gives the length of the curve from t=1 to t=3 ?

$\int_{1}^{3} \sqrt{1+9 t} d t$

$\int_{1}^{3} \sqrt{1+\frac{9}{16 t}} d t$

$\int_{1}^{3} \sqrt{16 t^{2}+9 t} d t$

$\int_{1}^{3} \sqrt{\left(2 t^{2}-1\right)^{2}+\left(3+2 t^{3 / 2}\right)^{2}} d t$

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