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

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

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integral from 1 to 0 of sqrt(x)

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

- \frac{2}{3}

Decimal

- 0.66666 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Apply the Power Rule

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

Compute the boundaries:

\frac{2}{3}

= - \frac{2}{3}

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