What is the integral from-5 to 3 of (x^3-2x+45)/2 ?

The integral from-5 to 3 of (x^3-2x+45)/2 is 120

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integral from-5 to 3 of (x^3-2x+45)/2

\int_{- 5}^{3} \frac{x ^{3} - 2 x + 45}{2} d x

120

Solution steps

\int_{- 5}^{3} \frac{x ^{3} - 2 x + 45}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- 5}^{3} x^{3} - 2 x + 45 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

= \frac{1}{2} (\int_{- 5}^{3} x^{3} d x - \int_{- 5}^{3} 2 x d x + \int_{- 5}^{3} 45 d x)

\int_{- 5}^{3} x^{3} d x = - 136

\int_{- 5}^{3} 2 x d x = - 16

\int_{- 5}^{3} 45 d x = 360

= \frac{1}{2} (- 136 - (- 16) + 360)

Simplify

\frac{1}{2} (- 136 - (- 16) + 360) : 120

= 120

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What is the integral from-5 to 3 of (x^3-2x+45)/2 ?
The integral from-5 to 3 of (x^3-2x+45)/2 is 120