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.
Remove unnecessary parentheses.
Subtract from to get .
Add and to get .
Since integration is linear, the integral of with respect to is .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Combine fractions.
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Write as a fraction with denominator .
Multiply and to get .
Since is constant with respect to , the integral of with respect to is .
Simplify the answer.
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Evaluate at and at .
Evaluate at and at .
Remove unnecessary parentheses.
Simplify each term.
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Simplify each term.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by to get .
Raise to the power of to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by to get .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
Add and to get .
Multiply by to get .
Multiply by to get .
Multiply by to get .
Add and to get .
Add and to get .
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