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

The integral from 2 to 1 of (x^2+3x-5) is -11/6

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

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

- \frac{11}{6}

Decimal Notation

- 1.83333 \dots

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

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

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

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

= - (\frac{7}{3} + \frac{9}{2} - 5)

Join

\frac{7}{3} + \frac{9}{2} - 5 : \frac{11}{6}

= - \frac{11}{6}

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What is the integral from 2 to 1 of (x^2+3x-5) ?
The integral from 2 to 1 of (x^2+3x-5) is -11/6