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

The integral from-2 to 3 of x+4-(x^2-2) is 125/6

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

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

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

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

Simplify

= \int_{- 2}^{3} - x^{2} + x + 6 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_{- 2}^{3} x^{2} d x + \int_{- 2}^{3} x d x + \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

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

\int_{- 2}^{3} 6 d x = 30

= - \frac{35}{3} + \frac{5}{2} + 30

Simplify

- \frac{35}{3} + \frac{5}{2} + 30 : \frac{125}{6}

= \frac{125}{6}

\int_{0}^{3} x^{3} - 4 x^{2} + 4 x d x

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\int_{\frac{π}{3}}^{\frac{π}{2}} cos^{3} (x) d x

\int_{- 2}^{2} e^{c o s (x)} sin (x) d x

What is the integral from-2 to 3 of x+4-(x^2-2) ?
The integral from-2 to 3 of x+4-(x^2-2) is 125/6