What is the integral from 2 to 5 of (2+2t+3t^2) ?

The integral from 2 to 5 of (2+2t+3t^2) is 144

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integral from 2 to 5 of (2+2t+3t^2)

\int_{2}^{5} (2 + 2 t + 3 t^{2}) d t

144

Solution steps

\int_{2}^{5} 2 + 2 t + 3 t^{2} d t

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}^{5} 2 d t + \int_{2}^{5} 2 t d t + \int_{2}^{5} 3 t^{2} d t

\int_{2}^{5} 2 d t = 6

\int_{2}^{5} 2 t d t = 21

\int_{2}^{5} 3 t^{2} d t = 117

= 6 + 21 + 117

Simplify

= 144

What is the integral from 2 to 5 of (2+2t+3t^2) ?
The integral from 2 to 5 of (2+2t+3t^2) is 144