What is the integral from-1 to 2 of (-x^2+4)-(-x+2) ?

The integral from-1 to 2 of (-x^2+4)-(-x+2) is 9/2

Popular >

integral from-1 to 2 of (-x^2+4)-(-x+2)

\int_{- 1}^{2} (- x^{2} + 4) - (- x + 2) d x

\frac{9}{2}

Decimal Notation

4.5

Solution steps

\int_{- 1}^{2} - x^{2} + 4 - (- x + 2) d x

Simplify

= \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_{0.5}^{1} \frac{ln ( x )}{4 x} d x

\int_{1}^{x} x^{4} + 1 d x

\int_{- 2}^{2} 4 x y^{3} d y

\int_{0}^{1} x^{3} + \frac{x ^{4}}{2} d x

\int_{0}^{1} 5 x^{2} e^{x^{3}} d x

What is the integral from-1 to 2 of (-x^2+4)-(-x+2) ?
The integral from-1 to 2 of (-x^2+4)-(-x+2) is 9/2