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

The integral from-2 to 2 of (1+x+x^2+x^3) is 28/3

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

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

\frac{28}{3}

Decimal

9.33333 \dots

Solution steps

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

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

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

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} x^{3} d x = 0

= 4 + 0 + \frac{16}{3} + 0

Simplify

4 + 0 + \frac{16}{3} + 0 : \frac{28}{3}

= \frac{28}{3}

What is the integral from-2 to 2 of (1+x+x^2+x^3) ?
The integral from-2 to 2 of (1+x+x^2+x^3) is 28/3