What is the integral from 1 to 5 of (3x^2+4x+1) ?

The integral from 1 to 5 of (3x^2+4x+1) is 176

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integral from 1 to 5 of (3x^2+4x+1)

\int_{1}^{5} (3 x^{2} + 4 x + 1) d x

176

Solution steps

\int_{1}^{5} 3 x^{2} + 4 x + 1 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}^{5} 3 x^{2} d x + \int_{1}^{5} 4 x d x + \int_{1}^{5} 1 d x

\int_{1}^{5} 3 x^{2} d x = 124

\int_{1}^{5} 4 x d x = 48

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

= 124 + 48 + 4

Simplify

= 176

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What is the integral from 1 to 5 of (3x^2+4x+1) ?
The integral from 1 to 5 of (3x^2+4x+1) is 176