# Need Practical Example! Very Strange.

• Jan 2nd 2009, 04:48 AM
sash786
Need Practical Example! Very Strange.
Hi everyone!
In Multivariable calculus we say for integration that.
Derivative --> is rate of change
Anti-Derivative(integral) --> Area Under the graph

Now
Integral is opposite of derivative
So
I need a practical example in which if we reverse the rate of change we get area?
for eg
iF plane is flying and if we take rate of change of flight then how to reverse it and get area?

I am not getting it!(Worried)
• Jan 2nd 2009, 05:27 AM
HallsofIvy
Quote:

Originally Posted by sash786
Hi everyone!
In Multivariable calculus we say for integration that.
Derivative --> is rate of change
Anti-Derivative(integral) --> Area Under the graph

No, we don't say that- certainly not in "multivariable" calculus. In single variable calculus, a common application of the integral is "area under the graph" but in multivariable calculus a graph does not have an "area" under it- it has a volume.

Quote:

Now
Integral is opposite of derivative
So
I need a practical example in which if we reverse the rate of change we get area?
for eg
iF plane is flying and if we take rate of change of flight then how to reverse it and get area?

I am not getting it!(Worried)
The "rate of change of flight" doesn't make sense. If you mean the "rate of change of distance flown" then that is the speed. "Reversing" it means going from speed to distance flown. it has nothing at all to do with area.

Again, finding "area under a graph" or "volume" are specific applications of the anti-derivative. You cannot just assert that every application of an anti-derivative must give an "area". I recommend that you go back and review the basic concepts of differentiation and integration.
• Jan 5th 2009, 02:06 AM
sash786
Quote:

The "rate of change of flight" doesn't make sense. If you mean the "rate of change of distance flown" then that is the speed. "Reversing" it means going from speed to distance flown. it has nothing at all to do with area.
It was just a try from my brain. I tried to make a practicle example.

Quote:

Again, finding "area under a graph" or "volume" are specific applications of the anti-derivative. You cannot just assert that every application of an anti-derivative must give an "area".
Oh yes! I know but i need just a single practicle example in which reverse of rate of change give area or volume. That's it .Its simple.