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

The integral from 1 to 2 of (x^2-5x-3) is -49/6

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

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

- \frac{49}{6}

Decimal

- 8.16666 \dots

Solution steps

\int_{1}^{2} x^{2} - 5 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_{1}^{2} x^{2} d x - \int_{1}^{2} 5 x d x - \int_{1}^{2} 3 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} 3 d x = 3

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

Simplify

\frac{7}{3} - \frac{15}{2} - 3 : - \frac{49}{6}

= - \frac{49}{6}

What is the integral from 1 to 2 of (x^2-5x-3) ?
The integral from 1 to 2 of (x^2-5x-3) is -49/6