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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- Nov 18th 2008, 07:19 PMplstevensApproximate 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 - Nov 18th 2008, 07:40 PMTheEmptySet
Hello plstevens,

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

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

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

Plugging into the above formula we get

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

It is all down hillfrom here.

Good luck