What is the integral from-1 to 1 of x+2x^2-x^3+5x^4 ?

The integral from-1 to 1 of x+2x^2-x^3+5x^4 is 10/3

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integral from-1 to 1 of x+2x^2-x^3+5x^4

\int_{- 1}^{1} x + 2 x^{2} - x^{3} + 5 x^{4} d x

\frac{10}{3}

Decimal Notation

3.33333 \dots

Solution steps

\int_{- 1}^{1} x + 2 x^{2} - x^{3} + 5 x^{4} 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_{- 1}^{1} x d x + \int_{- 1}^{1} 2 x^{2} d x - \int_{- 1}^{1} x^{3} d x + \int_{- 1}^{1} 5 x^{4} d x

\int_{- 1}^{1} x d x = 0

\int_{- 1}^{1} 2 x^{2} d x = \frac{4}{3}

\int_{- 1}^{1} x^{3} d x = 0

\int_{- 1}^{1} 5 x^{4} d x = 2

= 0 + \frac{4}{3} - 0 + 2

Simplify

0 + \frac{4}{3} - 0 + 2 : \frac{10}{3}

= \frac{10}{3}

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

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\int_{- π}^{0} 2 x^{4} d x

\int_{- 3}^{5} 2 x + 15 - x^{2} d x

\int_{2}^{7} \frac{1}{x} d x

What is the integral from-1 to 1 of x+2x^2-x^3+5x^4 ?
The integral from-1 to 1 of x+2x^2-x^3+5x^4 is 10/3