Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only)

2.75

2.5

1

3

$\sqrt{148}$

$\sqrt{13}$

14

13

$t = \frac{1}{\sqrt{3}}$

$t = 0$

$t = 1$

$t = \sqrt{3}$

$\sec^3(t)$

$\sec(t)\tan(t)$

$\tan(t)$

$\cos(t)$

$\int_{0}^{1} \sqrt{4t^2 + 9t^4} dt$

$\int_{0}^{1} \sqrt{t^2 + t^3} dt$

$\int_{0}^{1} (4t^2 + 9t^4) dt$

$\int_{0}^{1} (2t + 3t^2) dt$

$\int_{0}^{\pi} \sqrt{e^{2t} \cos^2(t) + e^{2t} \sin^2(t)} dt$

$\int_{0}^{\pi} \sqrt{2e^{2t}} dt$

$\int_{0}^{\pi} \sqrt{e^{2t} (\cos(t) - \sin(t))^2 + e^{2t} (\sin(t) + \cos(t))^2} dt$

$\int_{0}^{\pi} \sqrt{e^{t} \cos(t) + e^{t} \sin(t)} dt$

$\vec{v}(t) = <3t^2, -e^{-t}>$, $\vec{a}(t) = <6t, e^{-t}>$

$\vec{v}(t) = <t^4/4, -e^{-t}>$, $\vec{a}(t) = <t^5/20, e^{-t}>$

$\vec{v}(t) = <3t^2, e^{-t}>$, $\vec{a}(t) = <6t, -e^{-t}>$

$\vec{v}(t) = <3t^2, -e^{-t}>$, $\vec{a}(t) = <6t, -e^{-t}>$

$\frac{dy}{dx} = t$

$\frac{dy}{dx} = \frac{1}{t}$

$\frac{dy}{dx} = \frac{1}{2t}$

$\frac{dy}{dx} = 2$

Concave Up

Concave Down

Neither Concave Up nor Concave Down

Cannot be determined

$\vec{v}(t) = <2t, \cos(t)>$

$\vec{v}(t) = <t^3/3, -\cos(t)>$

$\vec{v}(t) = <2, -\sin(t)>$

$\vec{v}(t) = <t, \cos(t)>$