What is the integral from 2 to 7 of (3x^2-6x+5) ?

The integral from 2 to 7 of (3x^2-6x+5) is 225

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integral from 2 to 7 of (3x^2-6x+5)

\int_{2}^{7} (3 x^{2} - 6 x + 5) d x

225

Solution steps

\int_{2}^{7} 3 x^{2} - 6 x + 5 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}^{7} 3 x^{2} d x - \int_{2}^{7} 6 x d x + \int_{2}^{7} 5 d x

\int_{2}^{7} 3 x^{2} d x = 335

\int_{2}^{7} 6 x d x = 135

\int_{2}^{7} 5 d x = 25

= 335 - 135 + 25

Simplify

= 225

What is the integral from 2 to 7 of (3x^2-6x+5) ?
The integral from 2 to 7 of (3x^2-6x+5) is 225