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

The integral from 0 to 1/2 of (2x) is 1/4

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integral from 0 to 1/2 of (2x)

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

\frac{1}{4}

Decimal Notation

0.25

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{1}{8}

= 2 \cdot \frac{1}{8}

Simplify

= \frac{1}{4}

\int_{- 1}^{2} 9 - x^{2} d x

\int_{1}^{10} \frac{20}{x} d x

\int_{- 2}^{3} 9 - x^{2} d x

\int_{e^{1}}^{e^{2}} \frac{1}{x ln ( x )} d x

\int_{0}^{3} - 9 - x^{2} d x

What is the integral from 0 to 1/2 of (2x) ?
The integral from 0 to 1/2 of (2x) is 1/4