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

The integral from 0 to 2 of 3x^3 is 12

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integral from 0 to 2 of 3x^3

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

12

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= 3 [\frac{x ^{4}}{4}]_{0}^{2}

Compute the boundaries:

4

= 3 \cdot 4

Simplify

= 12

\int_{0}^{1} 3^{x} e^{x} d x

\int_{1}^{x^{2}} e^{- t^{2}} d t

\int_{- 4}^{1} ∣ x + 2 ∣ d x

\int_{- 1}^{2} e^{3 x} d x

\int_{0}^{2} 8 r^{2} - 2 r^{4} d r

What is the integral from 0 to 2 of 3x^3 ?
The integral from 0 to 2 of 3x^3 is 12