# Calculus Examples

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The area of the region between the curves is defined as the integral of the upper curve minus the integral of the lower curve over each region. The regions are determined by the intersection points of the curves. This can be done algebraically or graphically.

Combine the integrals into a single integral.

Apply the distributive property.

Subtract from .

Add and .

Split the single integral into multiple integrals.

Since is constant with respect to , move out of the integral.

By the Power Rule, the integral of with respect to is .

Combine and .

Since is constant with respect to , move out of the integral.

Evaluate at and at .

Evaluate at and at .

Raise to the power of .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Raise to the power of .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Multiply by .

Add and .

Multiply by .

Multiply by .

Multiply by .

Add and .

Add and .