Calculus Examples

Evaluate the Integral integral from 0 to pi/4 of 7sec(x)tan(x) with respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Since the derivative of is , the integral of is .
Step 3
Simplify the answer.
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Step 3.1
Evaluate at and at .
Step 3.2
Simplify.
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Step 3.2.1
The exact value of is .
Step 3.2.2
The exact value of is .
Step 3.2.3
Multiply by .
Step 3.3
Simplify.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Multiply .
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Step 3.3.2.1
Combine and .
Step 3.3.2.2
Multiply by .
Step 3.3.3
Multiply by .
Step 3.4
Simplify each term.
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Step 3.4.1
Multiply by .
Step 3.4.2
Combine and simplify the denominator.
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Step 3.4.2.1
Multiply by .
Step 3.4.2.2
Raise to the power of .
Step 3.4.2.3
Raise to the power of .
Step 3.4.2.4
Use the power rule to combine exponents.
Step 3.4.2.5
Add and .
Step 3.4.2.6
Rewrite as .
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Step 3.4.2.6.1
Use to rewrite as .
Step 3.4.2.6.2
Apply the power rule and multiply exponents, .
Step 3.4.2.6.3
Combine and .
Step 3.4.2.6.4
Cancel the common factor of .
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Step 3.4.2.6.4.1
Cancel the common factor.
Step 3.4.2.6.4.2
Rewrite the expression.
Step 3.4.2.6.5
Evaluate the exponent.
Step 3.4.3
Cancel the common factor of and .
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Step 3.4.3.1
Factor out of .
Step 3.4.3.2
Cancel the common factors.
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Step 3.4.3.2.1
Factor out of .
Step 3.4.3.2.2
Cancel the common factor.
Step 3.4.3.2.3
Rewrite the expression.
Step 3.4.3.2.4
Divide by .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: