Question

Sketch the Region enclosed, draw a typical approximating rectangle (i), and find the area:
y=(x+3)^1/2 & y=(x+3)/2

Answer 1

The first one is a square root function with h=-3, meaning it's displaced 3 units to the left.

The second one is a line. y=x/2+3/2. So the slope is 1/2. When you graph them it looks something like this:



So graph it (more accurately than my drawing obviously) and draw rectangles to approximate the area.

Answer 2

got that

Answer 3

\[\int\limits_{-3}^{1} \sqrt{x+3} - (x+3)/2\]

Answer 4

and label the points

Answer 5

This is what I have so far?