/sci/ - Science & Math

[Anonymous No.8020080]

derivative is the rate of change

anti-derivative is ....

[Anonymous No.8020094]

>>8020080
Integration

[Anonymous No.8020096]

Are you having difficulty with the concept of anti-differentiation?

Think in terms of displacement, velocity, acceleration.

Consider the following:
[math]x(t)=\frac{1}{2}t^2+t+1[/math]
where x(t) is displacement in meters and t is time in seconds

When derived with respect to time,
[math]\frac{dx}{dt}=t+1 [/math]
This gives a function for velocity in meters per second, v(t).

When derived with respect to time again,
[math]\frac{dv}{dt}=1 [/math]
This gives a function for acceleration in meters per second squared.

When you anti-derive, you're simply going backwards, from acceleration to velocity to displacement.

I like to think that when you anti-derive (otherwise known as 'integrate'), you're adding a component of whatever you're integrating with respect to.

E.g. when you integrate an acceleration function with respect to time, you add a time component to the function.

[Anonymous No.8020099]

>>8020096
This is just application in physics, there is more to it.

[Anonymous No.8020101]

>>8020080
The change.

dx/dt=v(t)
dv/dt=a(t)
Go backwards

[Anonymous No.8020122]

Accumulated value.

[Anonymous No.8020126]

>>8020080
The antiderivative (i.e. indefinite integral) is essentially to be understood as a relation where change occurs as described by the relation which is given to you.

A definite integral is the total net increase (i.e. change) of a function within a given interval, where the rate of change of that function at any point is represented by the function which is given.