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

The integral from-1 to 5 of (x^3+x^2-1) is 192

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

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

192

Solution steps

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

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

\int_{- 1}^{5} x^{2} d x = 42

\int_{- 1}^{5} 1 d x = 6

= 156 + 42 - 6

Simplify

= 192

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What is the integral from-1 to 5 of (x^3+x^2-1) ?
The integral from-1 to 5 of (x^3+x^2-1) is 192