How integral of 0 is C???

Question

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)

score 2 · Answer 1 · answered Feb 07 '17 at 15:06

2

Fundamental theorem of calculus:

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

For your case:

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

answered Feb 07 '17 at 15:06

Simply Beautiful Art

76,603

what if there are no a and b. i mean no limits or boundings for a general solution – Tauqeer Hassan Feb 07 '17 at 15:09
1

@TauqeerHassan Then it does not represent area under a curve. – Simply Beautiful Art Feb 07 '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 07 '17 at 15:17
@TauqeerHassan Please see this: http://math.stackexchange.com/questions/109225/whats-the-connection-between-the-indefinite-integral-and-the-definite-integral – Simply Beautiful Art Feb 07 '17 at 15:20

score 2 · Answer 2 · answered Feb 07 '17 at 15:12

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.

How integral of 0 is C???

2 Answers2