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Math Help - Approximate the are...

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by plstevens View Post
    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.
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