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

The integral from 2 to 3 of (3x^3-2x^2+4) is 481/12

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

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

\frac{481}{12}

Decimal

40.08333 \dots

Solution steps

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

\int_{2}^{3} 3 x^{3} d x = \frac{195}{4}

\int_{2}^{3} 2 x^{2} d x = \frac{38}{3}

\int_{2}^{3} 4 d x = 4

= \frac{195}{4} - \frac{38}{3} + 4

Simplify

\frac{195}{4} - \frac{38}{3} + 4 : \frac{481}{12}

= \frac{481}{12}

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What is the integral from 2 to 3 of (3x^3-2x^2+4) ?
The integral from 2 to 3 of (3x^3-2x^2+4) is 481/12