What is the integral from 0 to 2 of (2x-1)^3 ?

The integral from 0 to 2 of (2x-1)^3 is 10

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integral from 0 to 2 of (2x-1)^3

\int_{0}^{2} (2 x - 1)^{3} d x

10

Solution steps

\int_{0}^{2} (2 x - 1)^{3} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

20

= \frac{1}{2} \cdot 20

Simplify

= 10

\int_{2}^{3} \frac{3 - x}{2} d x

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\int_{0}^{3} arctan (x) d x

What is the integral from 0 to 2 of (2x-1)^3 ?
The integral from 0 to 2 of (2x-1)^3 is 10