What is the integral from 1 to 2 of 3x^2-3x+1 ?

The integral from 1 to 2 of 3x^2-3x+1 is 7/2

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integral from 1 to 2 of 3x^2-3x+1

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

\frac{7}{2}

Decimal

3.5

Solution steps

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

\int_{1}^{2} 3 x^{2} d x = 7

\int_{1}^{2} 3 x d x = \frac{9}{2}

\int_{1}^{2} 1 d x = 1

= 7 - \frac{9}{2} + 1

Simplify

7 - \frac{9}{2} + 1 : \frac{7}{2}

= \frac{7}{2}

What is the integral from 1 to 2 of 3x^2-3x+1 ?
The integral from 1 to 2 of 3x^2-3x+1 is 7/2