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

The integral from 0 to 2 of 2pix(x^2) is 8pi

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

\int_{0}^{2} 2 π x (x^{2}) d x

8 π

Decimal Notation

25.13274 \dots

Solution steps

\int_{0}^{2} 2 π x x^{2} d x

Take the constant out:

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

= 2 π \cdot \int_{0}^{2} x x^{2} d x

Simplify

x x^{2} : x^{3}

= 2 π \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{0}^{2}

= 2 π [\frac{x ^{4}}{4}]_{0}^{2}

Compute the boundaries:

4

= 2 π 4

Simplify

= 8 π

\frac{d}{d x} (e^{x \cdot c o s (x)})

\int_{0}^{6} π (2 x)^{2} d x

\frac{d}{d x} (ln (\frac{x ^{2}}{x + 1}))

\int \frac{( cos ( x ) )}{( ( sin ^{2} ( x ) ) ^{\frac{1}{3}} )} d x

\frac{d}{d t} (t^{2} + 4 t)

What is the integral from 0 to 2 of 2pix(x^2) ?
The integral from 0 to 2 of 2pix(x^2) is 8pi