What is the integral from 1 to 4 of (3/2 x^2-2x) ?

The integral from 1 to 4 of (3/2 x^2-2x) is 33/2

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integral from 1 to 4 of (3/2 x^2-2x)

\int_{1}^{4} (\frac{3}{2} x^{2} - 2 x) d x

\frac{33}{2}

Decimal

16.5

Solution steps

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

\int_{1}^{4} \frac{3}{2} x^{2} d x = \frac{63}{2}

\int_{1}^{4} 2 x d x = 15

= \frac{63}{2} - 15

Simplify

\frac{63}{2} - 15 : \frac{33}{2}

= \frac{33}{2}

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\int_{0}^{1} x e^{- 1} d x

What is the integral from 1 to 4 of (3/2 x^2-2x) ?
The integral from 1 to 4 of (3/2 x^2-2x) is 33/2