# 2013F002/A8

### From CDS 130

# 1. Midterm Problems

mta*

# 2. Numerical Integration

Use vertical rectangles to estimate the areas of the objects shown on the following hand-outs. Use both the "middle" rule and the "left rule" for each.

- Hand-out #1: pdf version | svg version
- Hand-out #2: pdf version | svg version

# 3. Numerical Integration

In this problem, we are given an equation that represents the height so we can compute the area by hand calculations and by iteration.

- Compute the area between the lines y=0, x=3, and the curve y=0.3333·x
^{3}using rectangles of width 1. Use this graph paper and let 1 unit be the width of a square. Turn in your diagram at the start of class. Include your calculations on your paper. You do not need to put your answers to this question on your wiki page. - Write a program without a
`for`

to compute the area using w=1. - Write a program with a
`for`

to compute the area using w=1. - Repeat all of the above using using w = 0.5.