What is the integral from 2 to 5 of 6sqrt(x) ?

The integral from 2 to 5 of 6sqrt(x) is 2(10sqrt(5)-4sqrt(2))

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integral from 2 to 5 of 6sqrt(x)

\int_{2}^{5} 6 x d x

2 (105 - 42)

Decimal

33.40765 \dots

Solution steps

\int_{2}^{5} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{2}^{5} x d x

Apply the Power Rule

= 6 [\frac{2}{3} x^{\frac{3}{2}}]_{2}^{5}

Compute the boundaries:

\frac{10 5 - 4 2}{3}

= 6 \cdot \frac{10 5 - 4 2}{3}

Simplify

= 2 (105 - 42)

What is the integral from 2 to 5 of 6sqrt(x) ?
The integral from 2 to 5 of 6sqrt(x) is 2(10sqrt(5)-4sqrt(2))