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

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

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

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

10

Solution steps

\int_{- 1}^{1} (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

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