What is the integral from 1 to 2 of (3x-2)^3 ?

The integral from 1 to 2 of (3x-2)^3 is 85/4

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integral from 1 to 2 of (3x-2)^3

\int_{1}^{2} (3 x - 2)^{3} d x

\frac{85}{4}

Decimal

21.25

Solution steps

\int_{1}^{2} (3 x - 2)^{3} d x

Apply u-substitution

= \int_{1}^{4} \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}^{4} u^{3} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{255}{4}

= \frac{1}{3} \cdot \frac{255}{4}

Simplify

= \frac{85}{4}

What is the integral from 1 to 2 of (3x-2)^3 ?
The integral from 1 to 2 of (3x-2)^3 is 85/4