What is the integral from 0 to 3 of 2pix(3x) ?

The integral from 0 to 3 of 2pix(3x) is 54pi

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integral from 0 to 3 of 2pix(3x)

\int_{0}^{3} 2 π x (3 x) d x

54 π

Decimal

169.64600 \dots

Solution steps

\int_{0}^{3} 2 π x \cdot 3 x d x

Take the constant out:

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

= 2 π 3 \cdot \int_{0}^{3} xx d x

Simplify

= 6 π \cdot \int_{0}^{3} xx d x

Simplify

xx : x^{2}

= 6 π \cdot \int_{0}^{3} x^{2} d x

Apply the Power Rule

= 6 π [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= 6 π 9

Simplify

= 54 π

What is the integral from 0 to 3 of 2pix(3x) ?
The integral from 0 to 3 of 2pix(3x) is 54pi