What is the integral from 4 to 1 of-sqrt(x) ?

The integral from 4 to 1 of-sqrt(x) is 14/3

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integral from 4 to 1 of-sqrt(x)

\int_{4}^{1} - x d x

\frac{14}{3}

Decimal

4.66666 \dots

Solution steps

\int_{4}^{1} - x d x

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

= - \int_{1}^{4} - x d x

Take the constant out:

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

= - (- \int_{1}^{4} x d x)

Apply the Power Rule

: [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

= - (- [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4})

Simplify

= [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{14}{3}

= \frac{14}{3}

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What is the integral from 4 to 1 of-sqrt(x) ?
The integral from 4 to 1 of-sqrt(x) is 14/3