What is the integral from 1 to 4 of 8sqrt(x) ?

The integral from 1 to 4 of 8sqrt(x) is 112/3

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integral from 1 to 4 of 8sqrt(x)

\int_{1}^{4} 8 x d x

\frac{112}{3}

Decimal

37.33333 \dots

Solution steps

\int_{1}^{4} 8 x d x

Take the constant out:

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

= 8 \cdot \int_{1}^{4} x d x

Apply the Power Rule

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

= 8 [\frac{2}{3} x^{\frac{3}{2}}]_{1}^{4}

Compute the boundaries:

\frac{14}{3}

= 8 \cdot \frac{14}{3}

Simplify

= \frac{112}{3}

\int_{0}^{π} (sin (x) cos (x)) d x

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

\int_{1}^{5} ln (4 x) d x

\int_{1}^{3} (8 - 2 x) d x

What is the integral from 1 to 4 of 8sqrt(x) ?
The integral from 1 to 4 of 8sqrt(x) is 112/3