Calculus Examples

Evaluate the Integral integral from 0 to 16 of 3 square root of x with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Use to rewrite as .
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Simplify the answer.
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Step 4.1
Combine and .
Step 4.2
Substitute and simplify.
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Step 4.2.1
Evaluate at and at .
Step 4.2.2
Simplify.
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Step 4.2.2.1
Rewrite as .
Step 4.2.2.2
Apply the power rule and multiply exponents, .
Step 4.2.2.3
Cancel the common factor of .
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Step 4.2.2.3.1
Cancel the common factor.
Step 4.2.2.3.2
Rewrite the expression.
Step 4.2.2.4
Raise to the power of .
Step 4.2.2.5
Multiply by .
Step 4.2.2.6
Rewrite as .
Step 4.2.2.7
Apply the power rule and multiply exponents, .
Step 4.2.2.8
Cancel the common factor of .
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Step 4.2.2.8.1
Cancel the common factor.
Step 4.2.2.8.2
Rewrite the expression.
Step 4.2.2.9
Raising to any positive power yields .
Step 4.2.2.10
Multiply by .
Step 4.2.2.11
Cancel the common factor of and .
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Step 4.2.2.11.1
Factor out of .
Step 4.2.2.11.2
Cancel the common factors.
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Step 4.2.2.11.2.1
Factor out of .
Step 4.2.2.11.2.2
Cancel the common factor.
Step 4.2.2.11.2.3
Rewrite the expression.
Step 4.2.2.11.2.4
Divide by .
Step 4.2.2.12
Multiply by .
Step 4.2.2.13
Add and .
Step 4.2.2.14
Combine and .
Step 4.2.2.15
Multiply by .
Step 4.2.2.16
Cancel the common factor of and .
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Step 4.2.2.16.1
Factor out of .
Step 4.2.2.16.2
Cancel the common factors.
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Step 4.2.2.16.2.1
Factor out of .
Step 4.2.2.16.2.2
Cancel the common factor.
Step 4.2.2.16.2.3
Rewrite the expression.
Step 4.2.2.16.2.4
Divide by .
Step 5