What is the integral from 0 to pi/3 of 1/(cos(x)) ?

The integral from 0 to pi/3 of 1/(cos(x)) is ln(2+sqrt(3))

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integral from 0 to pi/3 of 1/(cos(x))

\int_{0}^{\frac{π}{3}} \frac{1}{cos ( x )} d x

ln (2 + 3)

Decimal

1.31695 \dots

Solution steps

\int_{0}^{\frac{π}{3}} \frac{1}{cos ( x )} d x

Rewrite using trig identities

= \int_{0}^{\frac{π}{3}} sec (x) d x

Use the common integral:

\int sec (x) d x = ln ∣ tan (x) + sec (x) ∣

= [ln ∣ tan (x) + sec (x) ∣]_{0}^{\frac{π}{3}}

Compute the boundaries:

ln (2 + 3)

= ln (2 + 3)

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What is the integral from 0 to pi/3 of 1/(cos(x)) ?
The integral from 0 to pi/3 of 1/(cos(x)) is ln(2+sqrt(3))