Calculus
# Definite Integrals

$y = f(x)$ is shown above. What is the value of $\int_0^6 f(x) dx?$

The graph of the function$\int_0^8 x dx,$ his approximation will be the sum of the areas of the 2 rectangles shown. Assuming all his work is correct, what will his approximation be?

Steve knows that if he uses right-hand endpoints with 2 subintervals to find a Riemann sum approximation of$\int_0^8 x dx.$

Morgan and Pat use right-hand endpoints to find Riemann sum approximations ofIf Morgan uses 2 subintervals, and Pat uses 4 subintervals, whose approximation is closer to the true value of the integral?

Ferb knows that $\int_0^8 x dx = 32,$ and is interested in how close a right-hand Reimann sum approximation to the integral can be.

Based on his work so far, if Ferb uses 32 subintervals, what will his approximation be?

Number of subintervals | Approximation | Error |

1 | 64 | 32 |

2 | 48 | 16 |

4 | 40 | 8 |

8 | 36 | 4 |

16 | 34 | 2 |

32 | ?? |

$A = \int_{1}^{2} x dx, \,\,\,\, B = \int_{1}^{2} x^2 dx$

Which of the following is true of $A$ and $B?$

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