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

The integral from-1 to 3 of (x^3+2x-5) is 8

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

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

8

Solution steps

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

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

\int_{- 1}^{3} 2 x d x = 8

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

= 20 + 8 - 20

Simplify

= 8

x \to 4 lim (x - 5)

\int - 2 x^{4} d x

y = x^{2} - 2 x, y = - x^{2} + 6 x

x \to 3 lim (- (\frac{2}{x - 3}))

f (x) = 7 e^{(3 x^{2} - 2 x + 7)}

What is the integral from-1 to 3 of (x^3+2x-5) ?
The integral from-1 to 3 of (x^3+2x-5) is 8