## The Distance the Particle Travels with Given Position Function x(t) = t^4 - 8t^2

**Problem**

Given the position function *x*(*t*) = *t*^{4} - 8*t*^{2}, find the distance that the particle travels at *t* = 0 to *t* = 4.

A. 160 | C. 140 |

B. 150 | D. 130 |

**Problem**

Given the position function *x*(*t*) = *t*^{4} - 8*t*^{2}, find the distance that the particle travels at *t* = 0 to *t* = 4.

A. 160 | C. 140 |

B. 150 | D. 130 |

The length of arc in rectangular coordinates is given by the following formulas:

$\displaystyle s = \int_{x_1}^{x_2} \sqrt{1 + \left( \dfrac{dy}{dx} \right)^2} \, dx$ and $\displaystyle s = \int_{y_1}^{y_2} \sqrt{1 + \left(\dfrac{dx}{dy} \right)^2} \, dy$

See the derivations here: http://www.mathalino.com/reviewer/integral-calculus/length-arc-xy-plane…

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**Problem 717**

Locate the centroid of the bent wire shown in Fig. P-717. The wire is homogeneous and of uniform cross-section.

The total surface area of the sphere is four times the area of great circle. To know more about great circle, see properties of a sphere. Given the radius r of the sphere, the total surface area is