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

The integral from 0 to 3 of 2pi(x)(2x) is 36pi

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

\int_{0}^{3} 2 π (x) (2 x) d x

36 π

Decimal Notation

113.09733 \dots

Solution steps

\int_{0}^{3} 2 π x \cdot 2 x d x

Take the constant out:

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

= 2 π 2 \cdot \int_{0}^{3} xx d x

Simplify

= 4 π \cdot \int_{0}^{3} xx d x

Simplify

xx : x^{2}

= 4 π \cdot \int_{0}^{3} x^{2} d x

Apply the Power Rule

: [\frac{x ^{3}}{3}]_{0}^{3}

= 4 π [\frac{x ^{3}}{3}]_{0}^{3}

Compute the boundaries:

9

= 4 π 9

Simplify

= 36 π

\frac{d}{d x} (e^{x} (x^{2} - 2 x + 2))

\int e^{s} sin (1 - s) d s

5 cos ((\frac{π}{4} x) + \frac{π}{4})

\frac{d}{d x} (3 x^{2} + y^{2} - 1)

\int_{0}^{1} (x - x^{4}) d x

What is the integral from 0 to 3 of 2pi(x)(2x) ?
The integral from 0 to 3 of 2pi(x)(2x) is 36pi