What is the integral from 0 to 5 of (x^4+5x-4) ?

The integral from 0 to 5 of (x^4+5x-4) is 1335/2

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integral from 0 to 5 of (x^4+5x-4)

\int_{0}^{5} (x^{4} + 5 x - 4) d x

\frac{1335}{2}

Decimal

667.5

Solution steps

\int_{0}^{5} x^{4} + 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_{0}^{5} x^{4} d x + \int_{0}^{5} 5 x d x - \int_{0}^{5} 4 d x

\int_{0}^{5} x^{4} d x = 625

\int_{0}^{5} 5 x d x = \frac{125}{2}

\int_{0}^{5} 4 d x = 20

= 625 + \frac{125}{2} - 20

Simplify

625 + \frac{125}{2} - 20 : \frac{1335}{2}

= \frac{1335}{2}

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What is the integral from 0 to 5 of (x^4+5x-4) ?
The integral from 0 to 5 of (x^4+5x-4) is 1335/2