Question

What is the physical significance of the +C that we add on when we get the indefinite integral? What is a circumstance we would use that?

Answer 1

Consider the function 2x+3. What's its derivative? It's just 2. What's the integral of 2? 2x+C since we don't know what that value is, but we know it's there.

Answer 2

Does that make sense? I can explain it better if you'd like. :)

Answer 3

I think I am with you but if you have more detail that might clear it on up

Answer 4

Let's consider the function \[2x^2+6x-7\] would you agree that's the same as this? \[2x^2+6x^1-7x^0\]when you take the derivative, you just get \[4x^1+6x^0+0x^{-1}\] So since the 0 cancels out the information lost in the derivative you end up not being able to recover that when you integrate.

Normally when you're integrating you don't have the derivative to see what your constant should be, unless you're given an initial value, which is a calculus 2 thing that you don't need to worry about yet!

Answer 5

Also, don't confuse this model for reality, it's just an example. The integral of x^-1, or 1/x, is ln(x). I don't want to confuse you too much though, so I thought I'd add this as an afterthought. If it helps it helps, if it doesn't it doesn't.

Answer 6

No you were a huge help Thanks!!!!... I have a nother question if you are willing
We have used antiderivatives to get the area under a curve. Is it possible to use antiderivatives in such a way as to get volume instead?

Answer 7

@Kainui

Answer 8

Yes, you can use antiderivatives to get volumes, and you probably will later in your class! A common example is using integrals to prove the volume of spheres, cylinders, and cones. You can actually rotate any function around the x or y axis to make a volume as well like this:




or whatever to make some cool shapes.