What is the integral from 1 to 4 of x^2-5x+4 ?

The integral from 1 to 4 of x^2-5x+4 is -9/2

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integral from 1 to 4 of x^2-5x+4

\int_{1}^{4} x^{2} - 5 x + 4 d x

- \frac{9}{2}

Decimal Notation

- 4.5

Solution steps

\int_{1}^{4} x^{2} - 5 x + 4 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}^{4} x^{2} d x - \int_{1}^{4} 5 x d x + \int_{1}^{4} 4 d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 5 x d x = \frac{75}{2}

\int_{1}^{4} 4 d x = 12

= 21 - \frac{75}{2} + 12

Simplify

21 - \frac{75}{2} + 12 : - \frac{9}{2}

= - \frac{9}{2}

x^{\frac{3}{2}} + x^{\frac{1}{2}}

x \to 1 lim (\frac{3 - x}{3 + x} e^{- x} cos (π x))

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 8}{x})

\int_{\frac{2}{4}}^{\frac{1}{2}} \frac{1}{x ^{5} 16 x ^{2} - 1} d x

x \to 0 - lim (x^{2} \cdot sin (\frac{1}{x}))

What is the integral from 1 to 4 of x^2-5x+4 ?
The integral from 1 to 4 of x^2-5x+4 is -9/2