Write down the equation for both curves. Call one curve F(x) and the other one G(x). Determine the range for the area calculation. Usually these three data parameters are given in a problem.
For example:
F(x) = x^2 + 5
G(x) = sin(x) + 1
From the range [0,2]; from zero to two.
Subtract the equations of F(x) minus the equation for G(x). If there are any similar algebraic terms, reduce them.
From the example:
F(x) - G(x) =
( x^2 + 5 ) - ( sin(x) + 1 ) =
x^2 - sin(x) + 5 - 1 =
x^2 - sin(x) + 4
Set up an integral to solve the reduced equation. Use calculus to solve the integral or use an online integrator to solve the integral. Evaluate the integral on the interval provided.
Integrate ( x^2 - sin(x) + 4 ) , evaluated from [0, 2] =
( ( x^3 /3 ) + 4x + cos(x) ), evaluated from [0, 2] =
( 2.66 + 8 + 0.99 ) - ( 0 + 0 + 1 ) =
11.65 - 1 =
10.65
Apply absolute value to the answer of the integral. Since areas represent real life values, they cannot be negative. In this case a negative value can mean we subtract the functions in the wrong order. The answer, after the absolute value, will be the area under the two curves.
Absolute Value ( 10.65 ) = 10.65