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

The integral from 0 to 3 of (2x^2) is 18

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

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

18

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

9

= 2 \cdot 9

Simplify

= 18

\int_{0}^{2} 500 e^{0.05 t} d t

\int_{0}^{2} 9 4 x + 1 d x

\int_{0}^{2} \frac{1}{x ^{3} - x} d x

\int_{6}^{22} 2 f (\frac{x}{2}) d x

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

What is the integral from 0 to 3 of (2x^2) ?
The integral from 0 to 3 of (2x^2) is 18