What is the integral from 0 to pi/4 of 3sec(θ)tan(θ) ?

The integral from 0 to pi/4 of 3sec(θ)tan(θ) is 3(sqrt(2)-1)

Popular >

integral from 0 to pi/4 of 3sec(θ)tan(θ)

\int_{0}^{\frac{π}{4}} 3 sec (θ) tan (θ) d θ

3 (2 - 1)

Decimal

1.24264 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 3 sec (θ) tan (θ) d θ

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{4}} sec (θ) tan (θ) d θ

Apply u-substitution

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

= 3 \cdot \int_{1}^{2} 1 d u

Integral of a constant:

\int a d x = a x

= 3 [1 \cdot u]_{1}^{2}

Simplify

= 3 [u]_{1}^{2}

Compute the boundaries:

2 - 1

= 3 (2 - 1)

\int_{2}^{4} 3 d x

\int_{- \frac{π}{6}}^{\frac{π}{6}} (sec^{2} (x)) d x

\int_{0}^{1} (x + y + z) d x

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

\int_{1}^{2} x e^{- 2 x^{2}} d x

What is the integral from 0 to pi/4 of 3sec(θ)tan(θ) ?
The integral from 0 to pi/4 of 3sec(θ)tan(θ) is 3(sqrt(2)-1)