What is the integral from 2 to 3 of (3x^2+4x+8) ?

The integral from 2 to 3 of (3x^2+4x+8) is 37

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integral from 2 to 3 of (3x^2+4x+8)

\int_{2}^{3} (3 x^{2} + 4 x + 8) d x

37

Solution steps

\int_{2}^{3} 3 x^{2} + 4 x + 8 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} 4 x d x + \int_{2}^{3} 8 d x

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

\int_{2}^{3} 4 x d x = 10

\int_{2}^{3} 8 d x = 8

= 19 + 10 + 8

Simplify

= 37

What is the integral from 2 to 3 of (3x^2+4x+8) ?
The integral from 2 to 3 of (3x^2+4x+8) is 37