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

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}

\frac{4}{s ^{3} + 4 s ^{2} + 8 s}

\frac{d y}{d t} + 0.5 t y - 4 t = 0

\int_{0}^{4} (4 x - 4 x) d x

\int \frac{x + 9}{2 x ^{3} - 8 x} d x

\int \frac{- x}{3} 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