What is the integral from 0 to 20 of sqrt(4+3x) ?

The integral from 0 to 20 of sqrt(4+3x) is 112

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integral from 0 to 20 of sqrt(4+3x)

\int_{0}^{20} 4 + 3 x d x

112

Solution steps

\int_{0}^{20} 4 + 3 x d x

Apply u-substitution

: \int_{4}^{64} \frac{u}{3} d u

= \int_{4}^{64} \frac{u}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{4}^{64} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{64}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{64}

Compute the boundaries:

336

= \frac{1}{3} \cdot 336

Simplify

= 112

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What is the integral from 0 to 20 of sqrt(4+3x) ?
The integral from 0 to 20 of sqrt(4+3x) is 112