What is the integral from 0 to 0.5 of 4x ?

The integral from 0 to 0.5 of 4x is 0.5

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integral from 0 to 0.5 of 4x

\int_{0}^{0.5} 4 x d x

0.5

Solution steps

\int_{0}^{0.5} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{0}^{0.5} x d x

Apply the Power Rule

= 4 [\frac{x ^{2}}{2}]_{0}^{0.5}

Simplify

= 4 [0.5 x^{2}]_{0}^{0.5}

Compute the boundaries:

0.125

= 4 \cdot 0.125

Simplify

= 0.5

What is the integral from 0 to 0.5 of 4x ?
The integral from 0 to 0.5 of 4x is 0.5