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

The integral from 1 to 2 of (3x^3+4x^2-3x+2) is 217/12

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

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

\frac{217}{12}

Decimal

18.08333 \dots

Solution steps

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

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

\int_{1}^{2} 4 x^{2} d x = \frac{28}{3}

\int_{1}^{2} 3 x d x = \frac{9}{2}

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

= \frac{45}{4} + \frac{28}{3} - \frac{9}{2} + 2

Simplify

\frac{45}{4} + \frac{28}{3} - \frac{9}{2} + 2 : \frac{217}{12}

= \frac{217}{12}

What is the integral from 1 to 2 of (3x^3+4x^2-3x+2) ?
The integral from 1 to 2 of (3x^3+4x^2-3x+2) is 217/12