integrate |sinx| from 0 to 13 pi/3

Answer 1

13π/3 = 4π + 1/3 π

And of course |sinx| has all your sine curves above the x-axis
see:
https://www.wolframalpha.com/input/?i=y+%3D+%7Csinx%7C+from+0+to+13%CF%80%2F3

so we need
4∫ sinx dx from 0 to π + ∫ sinx dx from 0 to π/3
= 4[-cosx] from 0 to π + [-cosx] from 0 to π/3
= 4(-cosπ - (-cos0)) + (-cos π/3 - (-cos0) )
= 4(1 +1) + (-1/2 + 1)
= 8 + 1/2
= 8 1/2
= 8.5

https://www.wolframalpha.com/input/?i=%E2%88%AB+%7Csinx%7C+from+0+to+13%CF%80%2F3