### Numerical Integration

Graphs a function f(x) and the area under the graph of f (x) for a given interval, and finds approximations to that area by the Trapezoid Rule and Simpson's Rule.
How to use   ||   Examples   ||   Other Notes

How to use
• Enter the function f (x) in the text input field marked "f (x)=" (Example: f (x)=4-x2)
• Click the "Graph" button (this button also refreshes the graph)
• Enter the endpoints of the interval [a,b] for the definite integral in the text input fields marked "a=" and "b=", and click the "Graph" button to refresh (Example: [a,b]=[-2,2])
• For each method, the "+" and "-" buttons under the label marked "n=" change the number of subintervals used for that method (Example: n=20 for both methods)
• To erase the graph and all input fields, setting the "n=" fields to default values, click the "Clear" button
The text input field for f (x) can accept a wide variety of expressions to represent functions, and the buttons under the graph allow various manipulations of the graph coordinates. The text input fields for a and b can accept real numbers in decimal notation.
Examples
 Polynomial: f (x)=4-x2 [a,b]=[-2,2] n=20 for both Exponential: f (x)=e2 [a,b]=[0,2] n=10 for both Trigonometric: f (x) = sin x [a,b]=[0,3.14159] n=10 for both

Other Notes
The area under the curve on the interval [a,b] shaded so that positive areas are blue and negative areas are red. The approximate area computed by each method is shown in the labels marked "Area=".