# Integral Calculus

**Problem**

Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.

A. 0.2027 | C. 0.2270 |

B. 0.2207 | D. 0.2072 |

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**Problem**

Find the equation of the curve passing through the point (3, 2) and having s slope 5*x*^{2} - *x* + 1 at every point (*x*, *y*).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$ | C. $y = 5x^3 - 2x^2 + x - 118$ |

B. $y = 5x^3 - 2x^2 + x - 31$ | D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$ |

**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 |

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**Problem**

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |

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