What is the integral from 2 to 3 of (3x^2-2x+7) ?

The integral from 2 to 3 of (3x^2-2x+7) is 21

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integral from 2 to 3 of (3x^2-2x+7)

\int_{2}^{3} (3 x^{2} - 2 x + 7) d x

21

Solution steps

\int_{2}^{3} 3 x^{2} - 2 x + 7 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^{2} d x - \int_{2}^{3} 2 x d x + \int_{2}^{3} 7 d x

\int_{2}^{3} 3 x^{2} d x = 19

\int_{2}^{3} 2 x d x = 5

\int_{2}^{3} 7 d x = 7

= 19 - 5 + 7

Simplify

= 21

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\int_{0}^{3} \frac{1}{( x + 5 ) ( x ^{2} + 9 )} d x

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

What is the integral from 2 to 3 of (3x^2-2x+7) ?
The integral from 2 to 3 of (3x^2-2x+7) is 21