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

The integral from-1 to 2 of-x^2+x+2 is 9/2

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integral from-1 to 2 of-x^2+x+2

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

\frac{9}{2}

Decimal Notation

4.5

Solution steps

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

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

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

\int_{- 1}^{2} 2 d x = 6

= - 3 + \frac{3}{2} + 6

Simplify

- 3 + \frac{3}{2} + 6 : \frac{9}{2}

= \frac{9}{2}

\int \frac{1}{( x ^{2} + 36 ) ^{\frac{3}{2}}} d x

\frac{\partial}{\partial y} ((t^{2} + y^{2})^{\frac{3}{2}})

f (x) = (2 x + 4)^{\frac{1}{5}}, at x = 1

y \to \infty lim (\frac{( y ^{2} - e ^{(6 y)} )}{( 4 y ^{2} + e ^{7 y} )})

h (t) = (t + 1)^{\frac{2}{3}} (2 t^{2} - 1)^{3}

What is the integral from-1 to 2 of-x^2+x+2 ?
The integral from-1 to 2 of-x^2+x+2 is 9/2