What is the integral from 0 to 4 of 5x^2 ?

The integral from 0 to 4 of 5x^2 is 320/3

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integral from 0 to 4 of 5x^2

\int_{0}^{4} 5 x^{2} d x

\frac{320}{3}

Solution steps

\int_{0}^{4} 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{4} x^{2} d x

Apply the Power Rule

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

= 5 [\frac{x ^{3}}{3}]_{0}^{4}

Compute the boundaries:

\frac{64}{3}

= 5 \cdot \frac{64}{3}

Simplify

= \frac{320}{3}

\int_{- 2}^{1} (x + 1)^{2} - 1 d x

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

\int_{0}^{1 - x} 1 d y

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

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

What is the integral from 0 to 4 of 5x^2 ?
The integral from 0 to 4 of 5x^2 is 320/3