What is the integral from 0 to pi/4 of sec(θ) ?

The integral from 0 to pi/4 of sec(θ) is ln(1+sqrt(2))

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integral from 0 to pi/4 of sec(θ)

\int_{0}^{\frac{π}{4}} sec (θ) d θ

ln (1 + 2)

Decimal

0.88137 \dots

Solution steps

\int_{0}^{\frac{π}{4}} sec (θ) d θ

Use the common integral:

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

= [ln ∣ tan (θ) + sec (θ) ∣]_{0}^{\frac{π}{4}}

Compute the boundaries:

ln (1 + 2)

= ln (1 + 2)

What is the integral from 0 to pi/4 of sec(θ) ?
The integral from 0 to pi/4 of sec(θ) is ln(1+sqrt(2))