What is the integral from 0 to 2 of 2t^7-6t^5+4t ?

The integral from 0 to 2 of 2t^7-6t^5+4t is 8

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integral from 0 to 2 of 2t^7-6t^5+4t

\int_{0}^{2} 2 t^{7} - 6 t^{5} + 4 t d t

8

Solution steps

\int_{0}^{2} 2 t^{7} - 6 t^{5} + 4 t 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_{0}^{2} 2 t^{7} d t - \int_{0}^{2} 6 t^{5} d t + \int_{0}^{2} 4 t d t

\int_{0}^{2} 2 t^{7} d t = 64

\int_{0}^{2} 6 t^{5} d t = 64

\int_{0}^{2} 4 t d t = 8

= 64 - 64 + 8

Simplify

= 8

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What is the integral from 0 to 2 of 2t^7-6t^5+4t ?
The integral from 0 to 2 of 2t^7-6t^5+4t is 8