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marigirl
 one year ago
The definite integral
Why do we not take into account the constant of integration when doing questions with a definite integral?
marigirl
 one year ago
The definite integral Why do we not take into account the constant of integration when doing questions with a definite integral?

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marigirl
 one year ago
Best ResponseYou've already chosen the best response.0Such as area under a curve

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0read this link: http://math.stackexchange.com/questions/156376/definiteintegralandconstantofintegration

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0I.e Area under graphs

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you will find that in trying to evaluate a definite integral you will subtract the constant.

marigirl
 one year ago
Best ResponseYou've already chosen the best response.0Right. . So isn't it good to write it ... or I guess it must be like a x and 1x thing

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0i find this link confusing [doesn't mean it is, of course] \[\int_{0}^{x} \ f(t) \ dt = F(x)  F(0) = F(x) + C\] if defined at 0 how does that help illustrate anything? i refer specifically to this bit: "In the case above, ∫x0f(x)dx, there is confusion because the same variable is used inside the integration as in the bounds. The bound variable x inside the integral is not the same as the free variable x in the limit. To reduce the confusion, your integral can also be written as ∫x0f(t)dt by renaming the bound variable. In any case, this is a definite integral."

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1it depends on the reason for integrating. if you are trying to find an antiderivative, then there are a family of functions that will work, and they differ by a constant. if you are trying to determine the area between curves ... you already have functions defined for you and you are actually working a limiting process of say a Reimann sum.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what set of functions have a derivative of: 2x? f(x) = x^2 + C  what is the area from x=0 to x=2, between the curves: y=2x and y=0? (2)^2  (0)^2 = 4

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1im not sure if the definite integral can be considered as some initial value related thing. but i think it has more to do with the way it works out from the limiting definition.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1hmm, try a test ... use the +C \[\int_{0}^{2}2x~dx=\large [x^2+C]_{0}^{2}=2^20^2+(CC)\] maybe, but i dont think its rigorous.
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