# Definite Integrals

### Quizzes

1. |
Use a left-hand sum with 3 sub-intervals to estimate the area between f ( x ) = |x| and the x-axis on the interval [-4,2]. |

2. |
Partial values of the function g are given in the table below.Use a left-hand sum with the sub-intervals suggested by the data in the table to estimate the area between the graph of |

3. |
Determine which formula produces a right-hand sum approximation to the area between f and the x-axis on [1,10].→[ f(3) + ( 2 ) + f (4) + f f (5) + f (6) + (7) +f (8) +f (9)]f Δ x |

4. |
Which of the following statements is true?→If f is increasing on [a,b] then LHS(2) will provide an underestimate for the area between f and the x-axis on [a,b]. |

5. |
Let and let R be the region between the graph of f and the x-axis on [2,4]. How many sub-intervals must we use to guarantee that the left-hand sum will be within .25 of the exact area of R?→more than 3 |

6. |
Which picture best illustrates the area accounted for by using MID(3) to approximate the area between f ( x ) and the x-axis on [a,b]?→ |

7. |
Let f ( x ) = sin x + 1. Use a trapezoid sum with 4 sub-intervals to estimate the area between f and the x-axis on [0,2π].→ |

8. |
Partial values of the function f are shown in the table below. We want to estimate the area between f and the x-axis on [0,4]. We can use the values in the table to find all but one of the following midpoint sums. Which midpoint sum cannot be found using the information in the table? →MID(4) |

9. |
For which of the following functions f will any midpoint sum give an overestimate of the area between f and the x-axis on [0,2]?→f ( x ) = x^{2} |

10. |
Let f be a non-negative function that is increasing and concave up. Let R be the region between the graph of f and the x-axis on [a,b]. Which of the following quantities is largest?→The area of R. |