# How integral of 0 is C??? [duplicate]

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Toady I read that integral of 0 is C. because integral = antiderivative.

How can this be true, because we know that an integral is the area under a curve...and there is no area under the line x = 0, then how its area will be any Constant(after integrating the curve)

## marked as duplicate by Rohan, Shailesh, Did, Ross Millikan, TheGeekGreekFeb 7 '17 at 17:29

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## 2 Answers

Fundamental theorem of calculus:

$$\int_a^bf(x)\ dx=F(b)-F(a)$$

For your case:

$$\int_a^b0\ dx=C-C=0$$

• what if there are no a and b. i mean no limits or boundings for a general solution – Tauqeer Hassan Feb 7 '17 at 15:09
• @TauqeerHassan Then it does not represent area under a curve. – Simply Beautiful Art Feb 7 '17 at 15:10
• can u differentiate me between definti and indefinte integrals and what type of integral will be in this question – Tauqeer Hassan Feb 7 '17 at 15:17
• @TauqeerHassan Please see this: math.stackexchange.com/questions/109225/… – Simply Beautiful Art Feb 7 '17 at 15:20

You're confusing definite and indefinite integrals.

A definite integral $\int_a^b \cdots dx$ can (under some common conditions) be interpreted as the area under a curve, but an indefinite integral $\int \cdots dx$ cannot -- it's not even a number but a function (well, a family of functions) defined simply by the requirement that its derivative must be the integrand.