What is the integral from 0 to 0.5 of 200x ?

The integral from 0 to 0.5 of 200x is 25

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integral from 0 to 0.5 of 200x

\int_{0}^{0.5} 200 x d x

25

Solution steps

\int_{0}^{0.5} 200 x d x

Take the constant out:

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

= 200 \cdot \int_{0}^{0.5} x d x

Apply the Power Rule

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

= 200 [\frac{x ^{2}}{2}]_{0}^{0.5}

Simplify

= 200 [0.5 x^{2}]_{0}^{0.5}

Compute the boundaries:

0.125

= 200 \cdot 0.125

Simplify

= 25

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What is the integral from 0 to 0.5 of 200x ?
The integral from 0 to 0.5 of 200x is 25