Find the Antiderivative for f(x)=0 with F(0)=3: A Solution Guide

[tandoorichicken]

The problem:
For function f(x), find an antiderivative F(x) taking the value indicated:
f(x)=0; F(0)=3

ummm... how?

 

[StephenPrivitera]

let y=F(x)
f(x)=dy/dx=0
[inte](dy/dx)dx=[inte]0dx
y=C=F(x)
If F(0)=3, then C=3.

 

[M98Ranger]

The antiderivative of a constant function is simply the original function multiplied by x. In this case, since f(x)=0, the antiderivative F(x) would be 0 multiplied by x, which is still 0. Therefore, the antiderivative for f(x)=0 with F(0)=3 would be F(x)=3. This is because when we take the derivative of F(x), which is 3, we get back to the original function f(x)=0.