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Thread: Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

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    Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

    Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
    f(x)=3x^2-2 from x=1 to x=5; n=4; use the right endpoints
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    Quote Originally Posted by plstevens View Post
    Approximate the area under the graph of f(x) and above the x-axis using n rectangles.
    f(x)=3x^2-2 from x=1 to x=5; n=4; use the right endpoints
    Hello plstevens,

    \int_{a}^{b}f(x)dx \approx \sum_{n=1}^{4}f(x_n)\Delta x

    Where \Delta x =\frac{b-a}{n}=\frac{5-1}{4}=1 and

    x_n=a+n \Delta x =1+n\Delta x \mbox{ for } n=1,2,3,4

    Plugging into the above formula we get


    \int_{a}^{b}f(x)dx \approx \sum_{n=1}^{4}f(x_n)\Delta x=f(2)+f(3)+f(4)+f(5)

    It is all down hillfrom here.

    Good luck
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