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

The integral from 0 to 1 of 2sqrt(x) is 4/3

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integral from 0 to 1 of 2sqrt(x)

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

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

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

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{1}

= 2 [\frac{2}{3} x^{\frac{3}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{3}

= 2 \cdot \frac{2}{3}

Simplify

= \frac{4}{3}

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

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\int_{5}^{0} ∣ 2 x - 5 ∣ d x

What is the integral from 0 to 1 of 2sqrt(x) ?
The integral from 0 to 1 of 2sqrt(x) is 4/3