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

The integral from 1 to 5 of (x^2-x+2) is 112/3

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

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

\frac{112}{3}

Decimal Notation

37.33333 \dots

Solution steps

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

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

\int_{1}^{5} x d x = 12

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

= \frac{124}{3} - 12 + 8

Simplify

\frac{124}{3} - 12 + 8 : \frac{112}{3}

= \frac{112}{3}

\int_{1}^{5} 9 - 6 x + x^{2} d x

\int_{4}^{9} \frac{9 x + 1}{x} d x

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

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

\int_{0}^{3} (5 x + 1) d x

What is the integral from 1 to 5 of (x^2-x+2) ?
The integral from 1 to 5 of (x^2-x+2) is 112/3