# Evaluate integral from 0 to pi/6 of sec(y) with respect to y

The integral of with respect to is .
Evaluate at and at .
Simplify.
The exact value of is .
The exact value of is .
The exact value of is .
The exact value of is .
The absolute value is the distance between a number and zero. The distance between and is .
The natural logarithm of is .
Multiply by .
Evaluate.
Simplify each term.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Combine the numerators over the common denominator.
Cancel the common factor of .
Cancel the common factor.
Divide by .
is approximately which is positive so remove the absolute value
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate integral from 0 to pi/6 of sec(y) with respect to y