What is the integral from 0 to 1 of sqrt(3x+3) ?

The integral from 0 to 1 of sqrt(3x+3) is (4sqrt(6)-2sqrt(3))/3

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integral from 0 to 1 of sqrt(3x+3)

\int_{0}^{1} 3 x + 3 d x

\frac{4 6 - 2 3}{3}

Decimal

2.11128 \dots

Solution steps

\int_{0}^{1} 3 x + 3 d x

Apply u-substitution

: \int_{3}^{6} \frac{u}{3} d u

= \int_{3}^{6} \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_{3}^{6} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{6}

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{3}^{6}

Compute the boundaries:

46 - 23

= \frac{1}{3} (46 - 23)

Simplify

= \frac{4 6 - 2 3}{3}

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What is the integral from 0 to 1 of sqrt(3x+3) ?
The integral from 0 to 1 of sqrt(3x+3) is (4sqrt(6)-2sqrt(3))/3