What is the integral from 0 to pi/3 of sec(θ) ?

The integral from 0 to pi/3 of sec(θ) is ln(2+sqrt(3))

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integral from 0 to pi/3 of sec(θ)

\int_{0}^{\frac{π}{3}} sec (θ) d θ

ln (2 + 3)

Decimal

1.31695 \dots

Solution steps

\int_{0}^{\frac{π}{3}} 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}{3}}

Compute the boundaries:

ln (2 + 3)

= ln (2 + 3)

\int_{- 1}^{2} \frac{1}{x ^{2} - 4} d x

\int_{1}^{x^{4}} sec (x) d x

\int_{0}^{x} \frac{1}{1 - t ^{2}} d t

\int_{1}^{x} \frac{10}{9 x ^{2}} d x

\int_{x - 3}^{x + 3} y d y

What is the integral from 0 to pi/3 of sec(θ) ?
The integral from 0 to pi/3 of sec(θ) is ln(2+sqrt(3))