Calculus Examples

Evaluate the Integral integral from pi/4 to pi/3 of sec(x)tan(x) with respect to x
Step 1
Since the derivative of is , the integral of is .
Step 2
Simplify the answer.
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Step 2.1
Evaluate at and at .
Step 2.2
Simplify.
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Step 2.2.1
The exact value of is .
Step 2.2.2
The exact value of is .
Step 2.3
Simplify each term.
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Step 2.3.1
Multiply by .
Step 2.3.2
Combine and simplify the denominator.
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Step 2.3.2.1
Multiply by .
Step 2.3.2.2
Raise to the power of .
Step 2.3.2.3
Raise to the power of .
Step 2.3.2.4
Use the power rule to combine exponents.
Step 2.3.2.5
Add and .
Step 2.3.2.6
Rewrite as .
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Step 2.3.2.6.1
Use to rewrite as .
Step 2.3.2.6.2
Apply the power rule and multiply exponents, .
Step 2.3.2.6.3
Combine and .
Step 2.3.2.6.4
Cancel the common factor of .
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Step 2.3.2.6.4.1
Cancel the common factor.
Step 2.3.2.6.4.2
Rewrite the expression.
Step 2.3.2.6.5
Evaluate the exponent.
Step 2.3.3
Cancel the common factor of .
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Step 2.3.3.1
Cancel the common factor.
Step 2.3.3.2
Divide by .
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: