What is the integral from 1 to 4 of x^2-3x+12 ?

The integral from 1 to 4 of x^2-3x+12 is 69/2

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integral from 1 to 4 of x^2-3x+12

\int_{1}^{4} x^{2} - 3 x + 12 d x

\frac{69}{2}

Decimal Notation

34.5

Solution steps

\int_{1}^{4} x^{2} - 3 x + 12 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} 3 x d x + \int_{1}^{4} 12 d x

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

\int_{1}^{4} 3 x d x = \frac{45}{2}

\int_{1}^{4} 12 d x = 36

= 21 - \frac{45}{2} + 36

Simplify

21 - \frac{45}{2} + 36 : \frac{69}{2}

= \frac{69}{2}

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\frac{d}{d x} (arctanh (3 x))

ln (\frac{x ^{2}}{2 x ^{2} + 3 x + 2})

What is the integral from 1 to 4 of x^2-3x+12 ?
The integral from 1 to 4 of x^2-3x+12 is 69/2