What is the integral from 0 to 1 of sqrt(1+15x) ?

The integral from 0 to 1 of sqrt(1+15x) is 14/5

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integral from 0 to 1 of sqrt(1+15x)

\int_{0}^{1} 1 + 15 x d x

\frac{14}{5}

Decimal

2.8

Solution steps

\int_{0}^{1} 1 + 15 x d x

Apply u-substitution

= \int_{1}^{16} \frac{u}{15} d u

Take the constant out:

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

= \frac{1}{15} \cdot \int_{1}^{16} u d u

Apply the Power Rule

= \frac{1}{15} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{16}

Compute the boundaries:

42

= \frac{1}{15} \cdot 42

Simplify

= \frac{14}{5}

What is the integral from 0 to 1 of sqrt(1+15x) ?
The integral from 0 to 1 of sqrt(1+15x) is 14/5