# Difference between revisions of "009B Sample Midterm 1"

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== [[009B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] == | == [[009B_Sample Midterm 1,_Problem_2|<span class="biglink"><span style="font-size:80%"> Problem 2 </span>]] == | ||

− | <span class="exam"> | + | <span class="exam">Evaluate the indefinite and definite integrals. |

− | <span class="exam"> | + | <span class="exam">(a) <math>\int x^2\sqrt{1+x^3}~dx</math> |

− | + | <span class="exam">(b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math> | |

− | |||

− | <span class="exam"> | ||

− | |||

− | < | ||

== [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] == | == [[009B_Sample Midterm 1,_Problem_3|<span class="biglink"><span style="font-size:80%"> Problem 3 </span>]] == |

## Revision as of 16:02, 12 November 2017

**This is a sample, and is meant to represent the material usually covered in Math 9B for the midterm. An actual test may or may not be similar.**

**Click on the** ** boxed problem numbers to go to a solution.**

## Problem 1

Let .

(a) Compute the left-hand Riemann sum approximation of with boxes.

(b) Compute the right-hand Riemann sum approximation of with boxes.

(c) Express as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

## Problem 2

Evaluate the indefinite and definite integrals.

(a)

(b)

## Problem 3

Evaluate the indefinite and definite integrals.

(a)

(b)

## Problem 4

Evaluate the integral:

## Problem 5

Let .

(a) Compute the left-hand Riemann sum approximation of with boxes.

(b) Compute the right-hand Riemann sum approximation of with boxes.

(c) Express as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

**Contributions to this page were made by Kayla Murray**