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

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

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

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

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

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

\int_{1}^{5} 2 d x = 8

\int_{1}^{5} 3 x d x = 36

\int_{1}^{5} x^{2} d x = \frac{124}{3}

= 8 + 36 - \frac{124}{3}

Simplify

8 + 36 - \frac{124}{3} : \frac{8}{3}

= \frac{8}{3}

\frac{1}{10 x}

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\frac{d y}{d x} = \frac{x - 2}{y - 4}

\int x^{3} + 7 x - 5 x e^{- 2 x^{2}} d x

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