# 009B Sample Midterm 2

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**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

Consider the region bounded by and the -axis.

- a) Use four rectangles and a Riemann sum to approximate the area of the region . Sketch the region and the rectangles and indicate whether your rectangles overestimate or underestimate the area of .
- b) Find an expression for the area of the region as a limit. Do not evaluate the limit.

## Problem 2

This problem has three parts:

- a) State the Fundamental Theorem of Calculus.

- b) Compute .

- c) Evaluate .

## Problem 3

Evaluate

- a)

- b)

## Problem 4

Evaluate the integral:

## Problem 5

Evaluate the integral: