What is the integral from 0 to 6 of 6sin(0.3t) ?

The integral from 0 to 6 of 6sin(0.3t) is 24.54404…

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 6 of 6sin(0.3t)

\int_{0}^{6} 6 sin (0.3 t) d t

24.54404 \dots

Solution steps

\int_{0}^{6} 6 sin (0.3 t) d t

Take the constant out:

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

= 6 \cdot \int_{0}^{6} sin (0.3 t) d t

Apply u-substitution

: \int_{0}^{1.8} sin (u) \frac{1}{0.3} d u

= 6 \cdot \int_{0}^{1.8} sin (u) \frac{1}{0.3} d u

Take the constant out:

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

= 6 \cdot \frac{1}{0.3} \cdot \int_{0}^{1.8} sin (u) d u

Simplify

= 6 \cdot 3.33333 \dots \cdot \int_{0}^{1.8} sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= 6 \cdot 3.33333 \dots [- cos (u)]_{0}^{1.8}

Simplify

= 20 [- cos (u)]_{0}^{1.8}

Compute the boundaries:

1.22720 \dots

= 20 \cdot 1.22720 \dots

Simplify

= 24.54404 \dots

\int_{3}^{4} \frac{x ^{2} - 1}{x - 1} d x

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

\int_{0}^{π} sin^{2} (n) x d x

\int_{x}^{y} cos (e^{t}) d t

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

What is the integral from 0 to 6 of 6sin(0.3t) ?
The integral from 0 to 6 of 6sin(0.3t) is 24.54404…