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

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

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

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

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

Simplify

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

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

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

\int_{- 1}^{3} 3 d x = 12

= - \frac{28}{3} + 8 + 12

Simplify

- \frac{28}{3} + 8 + 12 : \frac{32}{3}

= \frac{32}{3}

\int_{0}^{\infty} 6 x e^{6 x} d x

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

\int_{1}^{2} 12 x^{3} + \frac{6}{x ^{2}} d x

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

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

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