# Math Help - Approximate the are...

1. ## Approximate the are...

Approximate the area under the graph f(x) and above the x-axis using n rectangles.
f(x)=(x^2)+2; interval [0,5]; n=5; use left endpoints

Now i missed class so i don't understand how to do this at all but i'm trying to do my homework, can someone help me please

2. Originally Posted by plstevens
Approximate the area under the graph f(x) and above the x-axis using n rectangles.
f(x)=(x^2)+2; interval [0,5]; n=5; use left endpoints

Now i missed class so i don't understand how to do this at all but i'm trying to do my homework, can someone help me please
You're going to make 5 rectangles to approximate the area under this curve. You're interval is going from x = [0,5] so conveniently you know the width of each rectangle is 1. The height of each rectangle if the height of f(x) somewhere in your interval. For instance, the first rectangle between [0,1] has many different heights in it. So we must pick one and use it as a good estimate. Using left-endpoints means to use f(x) at the beginning of each rectangle. So you'll use f(0), f(1), f(2), f(3), and f(4). There's right-endpoints also which just use the other end of the rectangle for an estimate of f(x).

So there are 5 rectangles. The first one is from [0,1] and we're using f(0)=0+2=2 as the height. So the area of the first rectangle is 5.

Now do the other 4 rectangles, add them all up, and you'll have your approximate area.