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

The integral from-1 to 3 of u(1-2u) is -44/3

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integral from-1 to 3 of u(1-2u)

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

- \frac{44}{3}

Decimal Notation

- 14.66666 \dots

Solution steps

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

Expand

u (1 - 2 u) : u - 2 u^{2}

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int_{- 1}^{3} 2 u^{2} d u = \frac{56}{3}

= 4 - \frac{56}{3}

Simplify

4 - \frac{56}{3} : - \frac{44}{3}

= - \frac{44}{3}

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What is the integral from-1 to 3 of u(1-2u) ?
The integral from-1 to 3 of u(1-2u) is -44/3