Calculus Examples

Integrate Using Trig Substitution integral from 0 to 3 of x/( square root of 36-x^2) with respect to x
Step 1
Let , where . Then . Note that since , is positive.
Step 2
Simplify terms.
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Step 2.1
Simplify .
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Step 2.1.1
Simplify each term.
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Step 2.1.1.1
Apply the product rule to .
Step 2.1.1.2
Raise to the power of .
Step 2.1.1.3
Multiply by .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.1.4
Factor out of .
Step 2.1.5
Apply pythagorean identity.
Step 2.1.6
Rewrite as .
Step 2.1.7
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2
Cancel the common factor of .
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Step 2.2.1
Cancel the common factor.
Step 2.2.2
Rewrite the expression.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
The integral of with respect to is .
Step 5
Simplify.
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Step 5.1
Evaluate at and at .
Step 5.2
Simplify.
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Step 5.2.1
The exact value of is .
Step 5.2.2
The exact value of is .
Step 5.3
Simplify.
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Step 5.3.1
Apply the distributive property.
Step 5.3.2
Cancel the common factor of .
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Step 5.3.2.1
Move the leading negative in into the numerator.
Step 5.3.2.2
Factor out of .
Step 5.3.2.3
Cancel the common factor.
Step 5.3.2.4
Rewrite the expression.
Step 5.3.3
Multiply by .
Step 5.3.4
Multiply by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: