What is the integral from 0 to pi/4 of 1/(cos(θ)) ?

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

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integral from 0 to pi/4 of 1/(cos(θ))

\int_{0}^{\frac{π}{4}} \frac{1}{cos ( θ )} d θ

ln (1 + 2)

Decimal Notation

0.88137 \dots

Solution steps

\int_{0}^{\frac{π}{4}} \frac{1}{cos ( θ )} d θ

Rewrite using trig identities

= \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)

\int_{0}^{2} (2 t^{3} + t) d t

\int_{1}^{\infty} - x e^{- x} d x

\int_{0}^{1} 12 x (x - x^{2}) d x

\int_{2}^{4} \frac{x - 2}{x} d x

\int_{- 1}^{0} (2 t + 2)^{2} d t

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