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

The integral from-2 to 2 of (1-2x)^2 is 76/3

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

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

\frac{76}{3}

Decimal Notation

25.33333 \dots

Solution steps

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

Expand

(1 - 2 x)^{2} : 1 - 4 x + 4 x^{2}

= \int_{- 2}^{2} 1 - 4 x + 4 x^{2} d x

Apply the Sum Rule:

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

= \int_{- 2}^{2} 1 d x - \int_{- 2}^{2} 4 x d x + \int_{- 2}^{2} 4 x^{2} d x

\int_{- 2}^{2} 1 d x = 4

\int_{- 2}^{2} 4 x d x = 0

\int_{- 2}^{2} 4 x^{2} d x = \frac{64}{3}

= 4 - 0 + \frac{64}{3}

Simplify

4 - 0 + \frac{64}{3} : \frac{76}{3}

= \frac{76}{3}

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What is the integral from-2 to 2 of (1-2x)^2 ?
The integral from-2 to 2 of (1-2x)^2 is 76/3