What is the integral from 0 to pi/4 of 5sec(θ)tan(θ) ?

The integral from 0 to pi/4 of 5sec(θ)tan(θ) is 5(sqrt(2)-1)

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integral from 0 to pi/4 of 5sec(θ)tan(θ)

\int_{0}^{\frac{π}{4}} 5 sec (θ) tan (θ) d θ

5 (2 - 1)

Decimal

2.07106 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 5 sec (θ) tan (θ) d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int_{0}^{\frac{π}{4}} sec (θ) tan (θ) d θ

Apply u-substitution

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

= 5 \cdot \int_{1}^{2} 1 d u

Integral of a constant:

\int a d x = a x

= 5 [1 \cdot u]_{1}^{2}

Simplify

= 5 [u]_{1}^{2}

Compute the boundaries:

2 - 1

= 5 (2 - 1)

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What is the integral from 0 to pi/4 of 5sec(θ)tan(θ) ?
The integral from 0 to pi/4 of 5sec(θ)tan(θ) is 5(sqrt(2)-1)