What is the integral from 0 to 2 of 4x^2 ?

The integral from 0 to 2 of 4x^2 is 32/3

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integral from 0 to 2 of 4x^2

\int_{0}^{2} 4 x^{2} d x

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

\int_{0}^{2} 4 x^{2} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

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

Compute the boundaries:

\frac{8}{3}

= 4 \cdot \frac{8}{3}

Simplify

= \frac{32}{3}

\frac{\partial}{\partial x} (ln (1 - 2 x))

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

\frac{e ^{2 x + 1}}{2 x + 5}

\int_{0}^{2} x e^{- 4 x} d x

f (t) = t^{2} e^{t}

What is the integral from 0 to 2 of 4x^2 ?
The integral from 0 to 2 of 4x^2 is 32/3