What is the integral from 1 to 2 of (-x^2+5x-4) ?

The integral from 1 to 2 of (-x^2+5x-4) is 7/6

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integral from 1 to 2 of (-x^2+5x-4)

\int_{1}^{2} (- x^{2} + 5 x - 4) d x

\frac{7}{6}

Decimal

1.16666 \dots

Solution steps

\int_{1}^{2} - 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_{1}^{2} x^{2} d x + \int_{1}^{2} 5 x d x - \int_{1}^{2} 4 d x

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

\int_{1}^{2} 5 x d x = \frac{15}{2}

\int_{1}^{2} 4 d x = 4

= - \frac{7}{3} + \frac{15}{2} - 4

Simplify

- \frac{7}{3} + \frac{15}{2} - 4 : \frac{7}{6}

= \frac{7}{6}

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What is the integral from 1 to 2 of (-x^2+5x-4) ?
The integral from 1 to 2 of (-x^2+5x-4) is 7/6