What is the integral from 1 to 3 of (2x^2-12x+13) ?

The integral from 1 to 3 of (2x^2-12x+13) is -14/3

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integral from 1 to 3 of (2x^2-12x+13)

\int_{1}^{3} (2 x^{2} - 12 x + 13) d x

- \frac{14}{3}

Decimal Notation

- 4.66666 \dots

Solution steps

\int_{1}^{3} 2 x^{2} - 12 x + 13 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}^{3} 2 x^{2} d x - \int_{1}^{3} 12 x d x + \int_{1}^{3} 13 d x

\int_{1}^{3} 2 x^{2} d x = \frac{52}{3}

\int_{1}^{3} 12 x d x = 48

\int_{1}^{3} 13 d x = 26

= \frac{52}{3} - 48 + 26

Simplify

\frac{52}{3} - 48 + 26 : - \frac{14}{3}

= - \frac{14}{3}

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

(ln (x + 2))^{^{'}}

x \to 7 - lim (\frac{6 x}{x - 7})

\frac{d}{d x} (- 1.2 x^{2} + 9.6 x)

\frac{( 1 - e ^{- 5 s} )}{s ^{2}}

What is the integral from 1 to 3 of (2x^2-12x+13) ?
The integral from 1 to 3 of (2x^2-12x+13) is -14/3