Calculus Examples

Evaluate the Integral integral from 0 to 10 of 4x^2+7 with respect to x
Step 1
Split the single integral into multiple integrals.
Step 2
Since is constant with respect to , move out of the integral.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Combine and .
Step 5
Apply the constant rule.
Step 6
Substitute and simplify.
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Step 6.1
Evaluate at and at .
Step 6.2
Evaluate at and at .
Step 6.3
Simplify.
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Step 6.3.1
Raise to the power of .
Step 6.3.2
Raising to any positive power yields .
Step 6.3.3
Cancel the common factor of and .
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Step 6.3.3.1
Factor out of .
Step 6.3.3.2
Cancel the common factors.
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Step 6.3.3.2.1
Factor out of .
Step 6.3.3.2.2
Cancel the common factor.
Step 6.3.3.2.3
Rewrite the expression.
Step 6.3.3.2.4
Divide by .
Step 6.3.4
Multiply by .
Step 6.3.5
Add and .
Step 6.3.6
Combine and .
Step 6.3.7
Multiply by .
Step 6.3.8
Multiply by .
Step 6.3.9
Multiply by .
Step 6.3.10
Add and .
Step 6.3.11
To write as a fraction with a common denominator, multiply by .
Step 6.3.12
Combine and .
Step 6.3.13
Combine the numerators over the common denominator.
Step 6.3.14
Simplify the numerator.
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Step 6.3.14.1
Multiply by .
Step 6.3.14.2
Add and .
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Step 8
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