What is the integral from 0 to pi/4 of 6sec(x)tan(x) ?

The integral from 0 to pi/4 of 6sec(x)tan(x) is 6(sqrt(2)-1)

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integral from 0 to pi/4 of 6sec(x)tan(x)

\int_{0}^{\frac{π}{4}} 6 sec (x) tan (x) d x

6 (2 - 1)

Decimal Notation

2.48528 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 6 sec (x) tan (x) d x

Take the constant out:

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

= 6 \cdot \int_{0}^{\frac{π}{4}} sec (x) tan (x) d x

Apply u-substitution

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

= 6 \cdot \int_{1}^{2} 1 d u

Integral of a constant:

\int a d x = a x

= 6 [1 \cdot u]_{1}^{2}

Simplify

= 6 [u]_{1}^{2}

Compute the boundaries:

2 - 1

= 6 (2 - 1)

\int_{1}^{2} (4 x^{2} + \frac{8}{x ^{2}}) d x

\int_{- 2}^{1} (4 x^{2} + 1) d x

\int_{0}^{1} (t - 1) d t

\int_{0}^{1} x^{\frac{1}{4}} - x^{\frac{1}{2}} d x

\int_{0}^{3} π (3 x - x^{2})^{2} d x

What is the integral from 0 to pi/4 of 6sec(x)tan(x) ?
The integral from 0 to pi/4 of 6sec(x)tan(x) is 6(sqrt(2)-1)