What is the integral from 0 to 2 of 0.5x^2 ?

The integral from 0 to 2 of 0.5x^2 is 1.33333…

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integral from 0 to 2 of 0.5x^2

\int_{0}^{2} 0.5 x^{2} d x

1.33333 \dots

Solution steps

\int_{0}^{2} 0.5 x^{2} d x

Take the constant out:

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

= 0.5 \cdot \int_{0}^{2} x^{2} d x

Apply the Power Rule

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

= 0.5 [\frac{x ^{3}}{3}]_{0}^{2}

Simplify

= 0.5 [0.33333 \dots x^{3}]_{0}^{2}

Compute the boundaries:

2.66666 \dots

= 0.5 \cdot 2.66666 \dots

Simplify

= 1.33333 \dots

\int_{0}^{1} x \frac{2 ( x + 1 )}{3} d x

\int_{1}^{1.5} \frac{3}{8} x^{2} d x

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\int_{0}^{3} 6 x ln (x) d x

What is the integral from 0 to 2 of 0.5x^2 ?
The integral from 0 to 2 of 0.5x^2 is 1.33333…