What is the integral from 0 to 1/2 of 30x ?

The integral from 0 to 1/2 of 30x is 15/4

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integral from 0 to 1/2 of 30x

\int_{0}^{\frac{1}{2}} 30 x d x

\frac{15}{4}

Decimal Notation

3.75

Solution steps

\int_{0}^{\frac{1}{2}} 30 x d x

Take the constant out:

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

= 30 \cdot \int_{0}^{\frac{1}{2}} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{\frac{1}{2}}

= 30 [\frac{x ^{2}}{2}]_{0}^{\frac{1}{2}}

Compute the boundaries:

\frac{1}{8}

= 30 \cdot \frac{1}{8}

Simplify

= \frac{15}{4}

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What is the integral from 0 to 1/2 of 30x ?
The integral from 0 to 1/2 of 30x is 15/4