Asked by singh
integrate |sinx| from 0 to 13 pi/3
Answers
Answered by
Reiny
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
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
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