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Invoking deep thoughts: Integration

Why don't we add a constant of integration when integrating the second function while applying integration by parts? I'm searching for a perfectly logical answer

Note by Mayank Singh
1 year, 8 months ago

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What is "the second function"? On \(\int u \, dv = uv - \int v \, du\), is the second function \(v\) or \(v \, du\)? Ivan Koswara · 1 year, 8 months ago

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@Ivan Koswara The second function is 'dv', the function whose integral is 'v' Sanchit Aggarwal · 1 year, 8 months ago

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It will not affect the final answer. You can try it out yourself. The extra part, if you think there will be any, will get cancelled out at the end. Sanchit Aggarwal · 1 year, 8 months ago

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@Sanchit Aggarwal What if I took different constants while integrating

P.S. You have to integrate g(x) twice while applying by parts Mayank Singh · 1 year, 8 months ago

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@Mayank Singh Ofcourse you cannot take different constants. You are integrating only one function, no matter twice. It should be the same general constt., or no constant at all.

P.s. refer to the derivation of the formula once Sanchit Aggarwal · 1 year, 8 months ago

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Thanks for asking this question, I had the same one in my mind! Swapnil Das · 1 year, 8 months ago

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@Swapnil Das Well I've reasoned something out... I'm waiting for some other replies Mayank Singh · 1 year, 8 months ago

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Comment deleted Jul 07, 2015

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@Swapnil Das Just last year Mayank Singh · 1 year, 8 months ago

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