Calculus Examples

Evaluate the Integral integral from 2 to 4 of (1/2x^3-3x+2) with respect to x
Step 1
Remove parentheses.
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
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
Substitute and simplify.
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Step 9.1
Evaluate at and at .
Step 9.2
Evaluate at and at .
Step 9.3
Evaluate at and at .
Step 9.4
Simplify.
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Step 9.4.1
Raise to the power of .
Step 9.4.2
Combine and .
Step 9.4.3
Cancel the common factor of and .
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Step 9.4.3.1
Factor out of .
Step 9.4.3.2
Cancel the common factors.
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Step 9.4.3.2.1
Factor out of .
Step 9.4.3.2.2
Cancel the common factor.
Step 9.4.3.2.3
Rewrite the expression.
Step 9.4.3.2.4
Divide by .
Step 9.4.4
Raise to the power of .
Step 9.4.5
Multiply by .
Step 9.4.6
Combine and .
Step 9.4.7
Cancel the common factor of and .
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Step 9.4.7.1
Factor out of .
Step 9.4.7.2
Cancel the common factors.
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Step 9.4.7.2.1
Factor out of .
Step 9.4.7.2.2
Cancel the common factor.
Step 9.4.7.2.3
Rewrite the expression.
Step 9.4.7.2.4
Divide by .
Step 9.4.8
Subtract from .
Step 9.4.9
Combine and .
Step 9.4.10
Cancel the common factor of and .
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Step 9.4.10.1
Factor out of .
Step 9.4.10.2
Cancel the common factors.
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Step 9.4.10.2.1
Factor out of .
Step 9.4.10.2.2
Cancel the common factor.
Step 9.4.10.2.3
Rewrite the expression.
Step 9.4.10.2.4
Divide by .
Step 9.4.11
Raise to the power of .
Step 9.4.12
Cancel the common factor of and .
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Step 9.4.12.1
Factor out of .
Step 9.4.12.2
Cancel the common factors.
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Step 9.4.12.2.1
Factor out of .
Step 9.4.12.2.2
Cancel the common factor.
Step 9.4.12.2.3
Rewrite the expression.
Step 9.4.12.2.4
Divide by .
Step 9.4.13
Raise to the power of .
Step 9.4.14
Cancel the common factor of and .
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Step 9.4.14.1
Factor out of .
Step 9.4.14.2
Cancel the common factors.
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Step 9.4.14.2.1
Factor out of .
Step 9.4.14.2.2
Cancel the common factor.
Step 9.4.14.2.3
Rewrite the expression.
Step 9.4.14.2.4
Divide by .
Step 9.4.15
Multiply by .
Step 9.4.16
Subtract from .
Step 9.4.17
Multiply by .
Step 9.4.18
Subtract from .
Step 9.4.19
Multiply by .
Step 9.4.20
Multiply by .
Step 9.4.21
Subtract from .
Step 9.4.22
Add and .
Step 10