What is the integral from-5 to 5 of (x^4+4x^2) ?

The integral from-5 to 5 of (x^4+4x^2) is 4750/3

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integral from-5 to 5 of (x^4+4x^2)

\int_{- 5}^{5} (x^{4} + 4 x^{2}) d x

\frac{4750}{3}

Decimal Notation

1583.33333 \dots

Solution steps

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

\int_{- 5}^{5} x^{4} d x = 1250

\int_{- 5}^{5} 4 x^{2} d x = \frac{1000}{3}

= 1250 + \frac{1000}{3}

Simplify

1250 + \frac{1000}{3} : \frac{4750}{3}

= \frac{4750}{3}

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What is the integral from-5 to 5 of (x^4+4x^2) ?
The integral from-5 to 5 of (x^4+4x^2) is 4750/3