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

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

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

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

- \frac{8}{3}

Decimal

- 2.66666 \dots

Solution steps

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

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

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

\int_{1}^{2} 8 d x = 8

= \frac{7}{3} + 3 - 8

Simplify

\frac{7}{3} + 3 - 8 : - \frac{8}{3}

= - \frac{8}{3}

\int_{1}^{2} \frac{1 + x ^{2}}{x ^{2}} d x

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\int_{1}^{2} (6 - 5 x)^{4} d x

\int_{3}^{15} \frac{1}{x} d x

\int_{1}^{8} 1 + x d x

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