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

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

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integral from 0 to pi/4 of sec(θ)tan(θ)

\int_{0}^{\frac{π}{4}} sec (θ) tan (θ) d θ

2 - 1

Decimal

0.41421 \dots

Solution steps

\int_{0}^{\frac{π}{4}} sec (θ) tan (θ) d θ

Apply u-substitution

: \int_{1}^{2} 1 d u

= \int_{1}^{2} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{1}^{2}

Simplify

= [u]_{1}^{2}

Compute the boundaries:

2 - 1

= 2 - 1

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\int_{- π}^{π} 4 sin (x) + cos (x) d x

\int_{0}^{1} sin (4 x) d x

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