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

The integral from 1 to 2 of (-x^2+3x-2) is 1/6

Popular >

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

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

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

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

\int_{1}^{2} x^{2} d x = \frac{7}{3}

\int_{1}^{2} 3 x d x = \frac{9}{2}

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

= - \frac{7}{3} + \frac{9}{2} - 2

Simplify

- \frac{7}{3} + \frac{9}{2} - 2 : \frac{1}{6}

= \frac{1}{6}

\int_{2}^{5} (x^{4} + 5 x^{2} + 5 + 9) d x

\int_{0}^{t} t e^{- 2 t} cos (t) d t

\int_{0}^{8} (8 - \frac{y ^{2}}{8}) d y

\int_{0}^{6} x^{2} + 8 d x

\int_{1}^{4} \frac{8}{x} d x

What is the integral from 1 to 2 of (-x^2+3x-2) ?
The integral from 1 to 2 of (-x^2+3x-2) is 1/6