What is the integral from 0 to 7 of pisin((pit)/7)+1 ?

The integral from 0 to 7 of pisin((pit)/7)+1 is 21

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integral from 0 to 7 of pisin((pit)/7)+1

\int_{0}^{7} π sin (\frac{π t}{7}) + 1 d t

21

Solution steps

\int_{0}^{7} π sin (\frac{π t}{7}) + 1 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}^{7} π sin (\frac{π t}{7}) d t + \int_{0}^{7} 1 d t

\int_{0}^{7} π sin (\frac{π t}{7}) d t = 14

\int_{0}^{7} 1 d t = 7

= 14 + 7

Simplify

= 21

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What is the integral from 0 to 7 of pisin((pit)/7)+1 ?
The integral from 0 to 7 of pisin((pit)/7)+1 is 21