What is the integral from 1 to 2 of (x^2-5x+3) ?

The integral from 1 to 2 of (x^2-5x+3) is -13/6

integral from 1 to 2 of (x^2-5x+3)

\int_{1}^{2} (x^{2} - 5 x + 3) d x

- \frac{13}{6}

Decimal

- 2.16666 \dots

Solution steps

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

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

\int_{1}^{2} 5 x d x = \frac{15}{2}

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

= \frac{7}{3} - \frac{15}{2} + 3

Simplify

\frac{7}{3} - \frac{15}{2} + 3 : - \frac{13}{6}

= - \frac{13}{6}

\int \frac{5}{x 4 - ln ^{2} ( x )} d x

\frac{d}{d x} (- 12 x cos (x^{2}) + 8 x^{3} sin (x^{2}))

in v erse l a pl a ce \frac{1}{s ^{2} + 6 s + 13}

d er i v a t i v e f (x) = x - 4

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

What is the integral from 1 to 2 of (x^2-5x+3) ?
The integral from 1 to 2 of (x^2-5x+3) is -13/6