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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{14}{3}

= - \frac{14}{3}

\int_{0}^{3} x (8 x^{2} + 9)^{\frac{1}{2}} d x

\int_{1}^{3} (2 x^{2} + 1) d x

\int_{2}^{6} 8 x - 24 d x

\int_{1}^{9} 2 x d x

\int_{1}^{8} x^{2} ln (x) d x

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