What is the integral from 1 to 4 of 3sqrt(x-1) ?

The integral from 1 to 4 of 3sqrt(x-1) is 6sqrt(3)

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integral from 1 to 4 of 3sqrt(x-1)

\int_{1}^{4} 3 x - 1 d x

63

Decimal Notation

10.39230 \dots

Solution steps

\int_{1}^{4} 3 x - 1 d x

Take the constant out:

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

= 3 \cdot \int_{1}^{4} x - 1 d x

Apply u-substitution

: \int_{0}^{3} u d u

= 3 \cdot \int_{0}^{3} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{3}

= 3 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{3}

Compute the boundaries:

23

= 3 \cdot 23

Simplify

= 63

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