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

The integral from 2 to 3 of (3x^2+2x+3) is 27

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

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

27

Solution steps

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

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

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

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

= 19 + 5 + 3

Simplify

= 27

y^{^{''}} + 11 y^{^{'}} + 24 y = 0

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What is the integral from 2 to 3 of (3x^2+2x+3) ?
The integral from 2 to 3 of (3x^2+2x+3) is 27