Calculus Examples

Evaluate the Integral integral from 0 to pi of 6e^x+9sin(x) 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
The integral of with respect to is .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
The integral of with respect to is .
Step 6
Simplify the answer.
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Step 6.1
Substitute and simplify.
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Step 6.1.1
Evaluate at and at .
Step 6.1.2
Evaluate at and at .
Step 6.1.3
Simplify.
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Step 6.1.3.1
Anything raised to is .
Step 6.1.3.2
Multiply by .
Step 6.2
The exact value of is .
Step 7
Simplify.
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Step 7.1
Simplify each term.
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Step 7.1.1
Apply the distributive property.
Step 7.1.2
Multiply by .
Step 7.1.3
Simplify each term.
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Step 7.1.3.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 7.1.3.2
The exact value of is .
Step 7.1.3.3
Multiply .
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Step 7.1.3.3.1
Multiply by .
Step 7.1.3.3.2
Multiply by .
Step 7.1.4
Add and .
Step 7.1.5
Multiply by .
Step 7.2
Add and .
Step 8
The result can be shown in multiple forms.
Exact Form:
Decimal Form: