Calculus Examples

Evaluate the Integral
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 .
By the Power Rule, the integral of with respect to is .
Simplify the answer.
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Write as a fraction with denominator .
Multiply and to get .
Evaluate at and at .
Evaluate at and at .
Raise to the power of to get .
One to any power is one.
Combine the numerators over the common denominator.
Multiply by to get .
Subtract from to get .
Write as a fraction with denominator .
Multiply and to get .
Multiply 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 .
One to any power is one.
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 .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
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 .
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Combine.
Multiply by to get .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Reorder terms.
The result can be shown in both exact and decimal forms.
Exact Form:
Decimal Form:
Mixed Number Form:
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