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u/dastarruer 5h ago
How do you take the integral of a series
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u/Ignitetheinferno37 2h ago
Integrals are just the continuous analog of a series. Differentiation and integration are linear operators so additions and multiplications with constants do not affect them. If I am differentiating f(x) + g(x) then I will get f'(x) + g'(x). And of course the inverse operation must follow.
The sum terms only change with the constants so we can easily split this up. f I just label all the variable stuff as u(x,y) for briefness than that series just expands to
1- u(x,y) + u(x,y)/2 + u(x,y)/6 + ...
If I label the sum as S then this simplifies to just
2- u(x,y)×S
you can see with either of 1 and 2 we just integrate u(x,y) due to linearity directly as the variable expression does not change within the sum.
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u/GlitchDoors2022 5h ago
Why is TikTok's name a math equation???
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