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

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

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

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

- 6

Solution steps

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

Simplify

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

\int_{0}^{3} x^{2} d x = 9

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

= - 9 + 3

Simplify

= - 6

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