What is the integral from 0 to 1 of (3x-1)^3 ?

The integral from 0 to 1 of (3x-1)^3 is 5/4

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integral from 0 to 1 of (3x-1)^3

\int_{0}^{1} (3 x - 1)^{3} d x

\frac{5}{4}

Decimal

1.25

Solution steps

\int_{0}^{1} (3 x - 1)^{3} d x

Apply u-substitution

= \int_{- 1}^{2} \frac{u ^{3}}{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_{- 1}^{2} u^{3} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{15}{4}

= \frac{1}{3} \cdot \frac{15}{4}

Simplify

= \frac{5}{4}

What is the integral from 0 to 1 of (3x-1)^3 ?
The integral from 0 to 1 of (3x-1)^3 is 5/4