What is the integral from 0 to 1 of (5x^2-8x+3) ?

The integral from 0 to 1 of (5x^2-8x+3) is 2/3

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integral from 0 to 1 of (5x^2-8x+3)

\int_{0}^{1} (5 x^{2} - 8 x + 3) d x

\frac{2}{3}

Decimal

0.66666 \dots

Solution steps

\int_{0}^{1} 5 x^{2} - 8 x + 3 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}^{1} 5 x^{2} d x - \int_{0}^{1} 8 x d x + \int_{0}^{1} 3 d x

\int_{0}^{1} 5 x^{2} d x = \frac{5}{3}

\int_{0}^{1} 8 x d x = 4

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

= \frac{5}{3} - 4 + 3

Simplify

\frac{5}{3} - 4 + 3 : \frac{2}{3}

= \frac{2}{3}

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What is the integral from 0 to 1 of (5x^2-8x+3) ?
The integral from 0 to 1 of (5x^2-8x+3) is 2/3