Approximate the are...

• Nov 3rd 2008, 09:15 PM
plstevens
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
• Nov 3rd 2008, 09:28 PM
Jameson
Quote:

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.