What is the integral from 1 to 4 of (5x^2-8x+5) ?

The integral from 1 to 4 of (5x^2-8x+5) is 60

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integral from 1 to 4 of (5x^2-8x+5)

\int_{1}^{4} (5 x^{2} - 8 x + 5) d x

60

Solution steps

\int_{1}^{4} 5 x^{2} - 8 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_{1}^{4} 5 x^{2} d x - \int_{1}^{4} 8 x d x + \int_{1}^{4} 5 d x

\int_{1}^{4} 5 x^{2} d x = 105

\int_{1}^{4} 8 x d x = 60

\int_{1}^{4} 5 d x = 15

= 105 - 60 + 15

Simplify

= 60

What is the integral from 1 to 4 of (5x^2-8x+5) ?
The integral from 1 to 4 of (5x^2-8x+5) is 60