What is the integral from 3 to 1 of 5sqrt(x) ?

The integral from 3 to 1 of 5sqrt(x) is -5(2sqrt(3)-2/3)

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integral from 3 to 1 of 5sqrt(x)

\int_{3}^{1} 5 x d x

- 5 (23 - \frac{2}{3})

Decimal Notation

- 13.98717 \dots

Solution steps

\int_{3}^{1} 5 x d x

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

= - \int_{1}^{3} 5 x d x

Take the constant out:

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

= - 5 \cdot \int_{1}^{3} x d x

Apply the Power Rule

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

= - 5 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{3}

Compute the boundaries:

23 - \frac{2}{3}

= - 5 (23 - \frac{2}{3})

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What is the integral from 3 to 1 of 5sqrt(x) ?
The integral from 3 to 1 of 5sqrt(x) is -5(2sqrt(3)-2/3)