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In integration, what does the +c mean and why does it disappear if you have limits?

Integration is the opposite to differentiation, when you differentiate with a constant it disappears and so you have to add it back when you integrate. You know what shape it is, but you don't know how far up the y axis it is. That's what the +c signifies. 

+c disappears when you have limits because you add it in the upper limit and you take it away in the lower limit, no matter what the values of x. For example, if you were to integrate x between 2 and 3, you'd have to evaluate [(x^2)/2 + c] between the values of 2 and 3. 

You'd get [(3^2)/2 + c] - [(2^2)/2 + c]
This is the same as (9/2) - (4/2) + c - c = 5/2

This is true no matter what x you put in because +c isn't changed by x in any way.

Zachary H. A Level Maths tutor, GCSE Maths tutor, Mentoring .STEP. tu...

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