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

The integral from 1 to 3 of (2x^2-3x+1) is 22/3

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

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

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

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

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 3 x d x = 12

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

= \frac{52}{3} - 12 + 2

Simplify

\frac{52}{3} - 12 + 2 : \frac{22}{3}

= \frac{22}{3}

What is the integral from 1 to 3 of (2x^2-3x+1) ?
The integral from 1 to 3 of (2x^2-3x+1) is 22/3