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

The integral from 0 to 2 of 0.5x is 1

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integral from 0 to 2 of 0.5x

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

1

Solution steps

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

Apply the Power Rule

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

Simplify

= 0.5 [0.5 x^{2}]_{0}^{2}

Compute the boundaries:

2

= 0.5 \cdot 2

Simplify

= 1

What is the integral from 0 to 2 of 0.5x ?
The integral from 0 to 2 of 0.5x is 1