Calculus Examples

Evaluate the Integral pi integral from 0 to 2 of (4-x^2)^2 with respect to x
Step 1
Expand .
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Step 1.1
Rewrite as .
Step 1.2
Apply the distributive property.
Step 1.3
Apply the distributive property.
Step 1.4
Apply the distributive property.
Step 1.5
Move .
Step 1.6
Move .
Step 1.7
Multiply by .
Step 1.8
Multiply by .
Step 1.9
Multiply by .
Step 1.10
Multiply by .
Step 1.11
Multiply by .
Step 1.12
Use the power rule to combine exponents.
Step 1.13
Add and .
Step 1.14
Subtract from .
Step 1.15
Reorder and .
Step 1.16
Move .
Step 2
Split the single integral into multiple integrals.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Combine and .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
By the Power Rule, the integral of with respect to is .
Step 7
Combine and .
Step 8
Apply the constant rule.
Step 9
Simplify the answer.
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Step 9.1
Combine and .
Step 9.2
Substitute and simplify.
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Step 9.2.1
Evaluate at and at .
Step 9.2.2
Evaluate at and at .
Step 9.2.3
Simplify.
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Step 9.2.3.1
Raise to the power of .
Step 9.2.3.2
Multiply by .
Step 9.2.3.3
To write as a fraction with a common denominator, multiply by .
Step 9.2.3.4
Combine and .
Step 9.2.3.5
Combine the numerators over the common denominator.
Step 9.2.3.6
Simplify the numerator.
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Step 9.2.3.6.1
Multiply by .
Step 9.2.3.6.2
Add and .
Step 9.2.3.7
Raising to any positive power yields .
Step 9.2.3.8
Cancel the common factor of and .
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Step 9.2.3.8.1
Factor out of .
Step 9.2.3.8.2
Cancel the common factors.
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Step 9.2.3.8.2.1
Factor out of .
Step 9.2.3.8.2.2
Cancel the common factor.
Step 9.2.3.8.2.3
Rewrite the expression.
Step 9.2.3.8.2.4
Divide by .
Step 9.2.3.9
Multiply by .
Step 9.2.3.10
Add and .
Step 9.2.3.11
Multiply by .
Step 9.2.3.12
Add and .
Step 9.2.3.13
Raise to the power of .
Step 9.2.3.14
Raising to any positive power yields .
Step 9.2.3.15
Cancel the common factor of and .
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Step 9.2.3.15.1
Factor out of .
Step 9.2.3.15.2
Cancel the common factors.
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Step 9.2.3.15.2.1
Factor out of .
Step 9.2.3.15.2.2
Cancel the common factor.
Step 9.2.3.15.2.3
Rewrite the expression.
Step 9.2.3.15.2.4
Divide by .
Step 9.2.3.16
Multiply by .
Step 9.2.3.17
Add and .
Step 9.2.3.18
Combine and .
Step 9.2.3.19
Multiply by .
Step 9.2.3.20
Move the negative in front of the fraction.
Step 9.2.3.21
To write as a fraction with a common denominator, multiply by .
Step 9.2.3.22
To write as a fraction with a common denominator, multiply by .
Step 9.2.3.23
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 9.2.3.23.1
Multiply by .
Step 9.2.3.23.2
Multiply by .
Step 9.2.3.23.3
Multiply by .
Step 9.2.3.23.4
Multiply by .
Step 9.2.3.24
Combine the numerators over the common denominator.
Step 9.2.3.25
Simplify the numerator.
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Step 9.2.3.25.1
Multiply by .
Step 9.2.3.25.2
Multiply by .
Step 9.2.3.25.3
Subtract from .
Step 9.2.3.26
Combine and .
Step 9.2.3.27
Move to the left of .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Step 11