# Evaluate integral of x square root of 4-9x^2 with respect to x

Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Since is constant with respect to , the derivative of with respect to is .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Multiply by .
Subtract from .
Rewrite the problem using and .
Simplify.
Move the negative in front of the fraction.
Combine and .
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of the integral.
Rewrite as .
By the Power Rule, the integral of with respect to is .
Simplify.
Simplify.
Simplify.
Combine and .
Multiply and .
Multiply by .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Replace all occurrences of with .
Evaluate integral of x square root of 4-9x^2 with respect to x