What is the integral from 0 to 2 of (3x^2-5x+4) ?

The integral from 0 to 2 of (3x^2-5x+4) is 6

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integral from 0 to 2 of (3x^2-5x+4)

\int_{0}^{2} (3 x^{2} - 5 x + 4) d x

6

Solution steps

\int_{0}^{2} 3 x^{2} - 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}^{2} 3 x^{2} d x - \int_{0}^{2} 5 x d x + \int_{0}^{2} 4 d x

\int_{0}^{2} 3 x^{2} d x = 8

\int_{0}^{2} 5 x d x = 10

\int_{0}^{2} 4 d x = 8

= 8 - 10 + 8

Simplify

= 6

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What is the integral from 0 to 2 of (3x^2-5x+4) ?
The integral from 0 to 2 of (3x^2-5x+4) is 6