Areas Between Two Curves

Graphs two functions, f(x) and g(x), and the area between the graphs of these functions for a given interval, and computes the area using given antiderivatives.
How to use   ||   Examples   ||   Other Notes


How to use
The text input fields for f (x), F (x), g(x), and G(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.

For assistance checking the antiderivatives F (x) and G(x), try computing the derivatives F '(x) and G '(x) using the Derivative Calculator, and checking F '(x)=f (x) and G '(x)=g(x).


Examples
Polynomial:
f (x)=x3-x
F (x)=x4/4-x2/2    
g(x)=x
G(x)=x2/2
[a,b]=[-2,2]
Trigonometric:
f (x)= sin x
F (x)= cos x
g(x)= cos x
G(x)= -sin x
[a,b]=[0.7854,2.3562]

Other Notes
The graph shows f (x) and g(x), with the area between the curves on the interval [a,b] shaded so that positive areas are blue and negative areas are red. A label under the graph shows the net area between the curves.

In the "Polynomial" example above, the regions shaded have part with f (x) above g(x) (in blue) and part reversed (in red). The two areas are exactly the same, giving a value of zero for net area (blue area minus red area).