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

The integral from 1 to 5 of (x^3+x^2-x+2) is 580/3

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

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

\frac{580}{3}

Decimal

193.33333 \dots

Solution steps

\int_{1}^{5} x^{3} + 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^{3} 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^{3} d x = 156

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

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

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

= 156 + \frac{124}{3} - 12 + 8

Simplify

156 + \frac{124}{3} - 12 + 8 : \frac{580}{3}

= \frac{580}{3}

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What is the integral from 1 to 5 of (x^3+x^2-x+2) ?
The integral from 1 to 5 of (x^3+x^2-x+2) is 580/3