# Calculus Examples

Step 1
Use the Gini Index formula .
Step 2
Substitute for .
Step 3
Evaluate .
Split the single integral into multiple integrals.
By the Power Rule, the integral of with respect to is .
Combine and .
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Combine and .
Substitute and simplify.
Evaluate at and at .
Evaluate at and at .
Simplify.
One to any power is one.
Raising to any positive power yields .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
One to any power is one.
Raising to any positive power yields .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply by .
Multiply by .
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Subtract from .
Combine and .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Step 4
Convert to decimal.