What is the integral from 0 to pi/4 of 8sec(θ)tan(θ) ?

The integral from 0 to pi/4 of 8sec(θ)tan(θ) is 8(sqrt(2)-1)

Popular >

integral from 0 to pi/4 of 8sec(θ)tan(θ)

\int_{0}^{\frac{π}{4}} 8 sec (θ) tan (θ) d θ

8 (2 - 1)

Decimal Notation

3.31370 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 8 sec (θ) tan (θ) d θ

Take the constant out:

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

= 8 \cdot \int_{0}^{\frac{π}{4}} sec (θ) tan (θ) d θ

Apply u-substitution

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

= 8 \cdot \int_{1}^{2} 1 d u

Integral of a constant:

\int a d x = a x

= 8 [1 \cdot u]_{1}^{2}

Simplify

= 8 [u]_{1}^{2}

Compute the boundaries:

2 - 1

= 8 (2 - 1)

\int_{0}^{π} sin^{3} (\frac{t}{2}) d t

\int_{2}^{3} 0 d x

\int_{- \frac{π}{3}}^{\frac{π}{4}} cos (θ) d θ

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x

\int_{1}^{3} 5 x - x^{2} d x

What is the integral from 0 to pi/4 of 8sec(θ)tan(θ) ?
The integral from 0 to pi/4 of 8sec(θ)tan(θ) is 8(sqrt(2)-1)