Calculus Examples

Evaluate the Integral integral from 1 to 9 of square root of x with respect to x
Step 1
Use to rewrite as .
Step 2
By the Power Rule, the integral of with respect to is .
Step 3
Substitute and simplify.
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Step 3.1
Evaluate at and at .
Step 3.2
Simplify.
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Step 3.2.1
Rewrite as .
Step 3.2.2
Apply the power rule and multiply exponents, .
Step 3.2.3
Cancel the common factor of .
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Step 3.2.3.1
Cancel the common factor.
Step 3.2.3.2
Rewrite the expression.
Step 3.2.4
Raise to the power of .
Step 3.2.5
Combine and .
Step 3.2.6
Multiply by .
Step 3.2.7
Cancel the common factor of and .
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Step 3.2.7.1
Factor out of .
Step 3.2.7.2
Cancel the common factors.
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Step 3.2.7.2.1
Factor out of .
Step 3.2.7.2.2
Cancel the common factor.
Step 3.2.7.2.3
Rewrite the expression.
Step 3.2.7.2.4
Divide by .
Step 3.2.8
One to any power is one.
Step 3.2.9
Multiply by .
Step 3.2.10
To write as a fraction with a common denominator, multiply by .
Step 3.2.11
Combine and .
Step 3.2.12
Combine the numerators over the common denominator.
Step 3.2.13
Simplify the numerator.
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Step 3.2.13.1
Multiply by .
Step 3.2.13.2
Subtract from .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Step 5