What is the integral from 0 to 2 of 2x^3 ?

The integral from 0 to 2 of 2x^3 is 8

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integral from 0 to 2 of 2x^3

\int_{0}^{2} 2 x^{3} d x

8

Solution steps

\int_{0}^{2} 2 x^{3} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

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

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

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

\int \frac{1}{( x - 2 ) ( x + 2 )} d x

x \to 0 lim (\frac{100000}{x})

\int x^{6} ln (3 x) d x

ln (22 x)

sin (2 x) cos (2 x)

What is the integral from 0 to 2 of 2x^3 ?
The integral from 0 to 2 of 2x^3 is 8