What is the integral from-2 to 1 of (5z^2-7z+z) ?

The integral from-2 to 1 of (5z^2-7z+z) is 24

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integral from-2 to 1 of (5z^2-7z+z)

\int_{- 2}^{1} (5 z^{2} - 7 z + z) d z

24

Solution steps

\int_{- 2}^{1} 5 z^{2} - 7 z + z d z

Simplify

= \int_{- 2}^{1} 5 z^{2} - 6 z d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 2}^{1} 5 z^{2} d z - \int_{- 2}^{1} 6 z d z

\int_{- 2}^{1} 5 z^{2} d z = 15

\int_{- 2}^{1} 6 z d z = - 9

= 15 - (- 9)

Simplify

= 24

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What is the integral from-2 to 1 of (5z^2-7z+z) ?
The integral from-2 to 1 of (5z^2-7z+z) is 24