What is the integral from 0 to 3 of (1+6w^2-10w^4) ?

The integral from 0 to 3 of (1+6w^2-10w^4) is -429

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integral from 0 to 3 of (1+6w^2-10w^4)

\int_{0}^{3} (1 + 6 w^{2} - 10 w^{4}) d w

- 429

Solution steps

\int_{0}^{3} 1 + 6 w^{2} - 10 w^{4} d w

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}^{3} 1 d w + \int_{0}^{3} 6 w^{2} d w - \int_{0}^{3} 10 w^{4} d w

\int_{0}^{3} 1 d w = 3

\int_{0}^{3} 6 w^{2} d w = 54

\int_{0}^{3} 10 w^{4} d w = 486

= 3 + 54 - 486

Simplify

= - 429

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What is the integral from 0 to 3 of (1+6w^2-10w^4) ?
The integral from 0 to 3 of (1+6w^2-10w^4) is -429