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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to pi/4 of sec(x)

\int_{0}^{\frac{π}{4}} sec (x) d x

ln (1 + 2)

Decimal

0.88137 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 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}{4}}

Compute the boundaries:

ln (1 + 2)

= ln (1 + 2)

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