Find the area between two curves.

[Miike012]

given two function f and g in the closed interval a to b, the area would be

∫(f(x) - g(x))dx from a to b if f(x)≥g(x) for all x in [a,b].

My question is.. if I were given two function f and g in a given interval [a,b], what is the best way to dertermine if f(x)≥g(x) or vise versa? Would it be best to graph the two functions then visually evaluate it?
Im looking for better methods... any suggestions??

 

[SammyS]

given two function f and g in the closed interval a to b, the area would be

∫(f(x) - g(x))dx from a to b if f(x)≥g(x) for all x in [a,b].

My question is.. if I were given two function f and g in a given interval [a,b], what is the best way to determine if f(x)≥g(x) or vise versa? Would it be best to graph the two functions then visually evaluate it?
I'm looking for better methods... any suggestions??

A lot depends upon the functions.

If they're continuous, you could evaluate f & g at the end pints of the interval and also see if f=g anywhere in the interval.

You could solve the inequality f(x) > g(x) .

Graphing is not such a bad idea.