Calculus Examples

Evaluate the Integral integral from -pi/6 to pi/6 of 5sec(x)^2 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
The exact value of is .
Step 3.3
Simplify.
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Step 3.3.1
Add full rotations of until the angle is greater than or equal to and less than .
Step 3.3.2
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the fourth quadrant.
Step 3.3.3
The exact value of is .
Step 3.3.4
Multiply .
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Step 3.3.4.1
Multiply by .
Step 3.3.4.2
Multiply by .
Step 3.3.5
Combine the numerators over the common denominator.
Step 3.3.6
Add and .
Step 3.3.7
Multiply .
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Step 3.3.7.1
Combine and .
Step 3.3.7.2
Multiply by .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: