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

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

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

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

24.54404 \dots

Solution steps

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

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

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