What is the integral from-1 to 3 of (-3x^2+4x-5) ?

The integral from-1 to 3 of (-3x^2+4x-5) is -32

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integral from-1 to 3 of (-3x^2+4x-5)

\int_{- 1}^{3} (- 3 x^{2} + 4 x - 5) d x

- 32

Solution steps

\int_{- 1}^{3} - 3 x^{2} + 4 x - 5 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}^{3} 3 x^{2} d x + \int_{- 1}^{3} 4 x d x - \int_{- 1}^{3} 5 d x

\int_{- 1}^{3} 3 x^{2} d x = 28

\int_{- 1}^{3} 4 x d x = 16

\int_{- 1}^{3} 5 d x = 20

= - 28 + 16 - 20

Simplify

= - 32

What is the integral from-1 to 3 of (-3x^2+4x-5) ?
The integral from-1 to 3 of (-3x^2+4x-5) is -32