What is the integral from 0 to 4 of (4x^3-9x^2+2x-1) ?

The integral from 0 to 4 of (4x^3-9x^2+2x-1) is 76

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integral from 0 to 4 of (4x^3-9x^2+2x-1)

\int_{0}^{4} (4 x^{3} - 9 x^{2} + 2 x - 1) d x

76

Solution steps

\int_{0}^{4} 4 x^{3} - 9 x^{2} + 2 x - 1 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}^{4} 4 x^{3} d x - \int_{0}^{4} 9 x^{2} d x + \int_{0}^{4} 2 x d x - \int_{0}^{4} 1 d x

\int_{0}^{4} 4 x^{3} d x = 256

\int_{0}^{4} 9 x^{2} d x = 192

\int_{0}^{4} 2 x d x = 16

\int_{0}^{4} 1 d x = 4

= 256 - 192 + 16 - 4

Simplify

= 76

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What is the integral from 0 to 4 of (4x^3-9x^2+2x-1) ?
The integral from 0 to 4 of (4x^3-9x^2+2x-1) is 76