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This question already has an answer here:

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)

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

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Fundamental theorem of calculus:

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

For your case:

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

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

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