1. ## Line Integral

I have to find line integral for $\displaystyle F = [y^3, x^3]$ , $\displaystyle C$ the parabola $\displaystyle y=5x^2$ from $\displaystyle A: (0,0)$ to $\displaystyle B(2,20)$.

I have made the parametric equations to be $\displaystyle x=t$ and $\displaystyle y=5t^2$. What I dont understand is that in order to integrate I need just one value of a and b , i.e. the limits. How do I chnage the A and B coordinates in the form of limits ?

2. Originally Posted by Altair
I have to find line integral for $\displaystyle F = [y^3, x^3]$ , $\displaystyle C$ the parabola $\displaystyle y=5x^2$ from $\displaystyle A: (0,0)$ to $\displaystyle B(2,20)$.

I have made the parametric equations to be $\displaystyle x=t$ and $\displaystyle y=5t^2$. What I dont understand is that in order to integrate I need just one value of a and b , i.e. the limits. How do I chnage the A and B coordinates in the form of limits ?
t goes from 0 up to 2

can you finish now?

3. That is what I am asking actually. How can you tell that it goes from 0 to 2 ?

4. Originally Posted by Altair
That is what I am asking actually. How can you tell that it goes from 0 to 2 ?
$\displaystyle (0, 0) \Rightarrow x = 0$ and $\displaystyle y = 0$. But $\displaystyle x = t \Rightarrow 0 = t$. Check: $\displaystyle y = 5 t^2 = 0$.

$\displaystyle (2, 20) \Rightarrow x = 2$ and $\displaystyle y = 20$. But $\displaystyle x = t \Rightarrow 2 = t$. Check: $\displaystyle y = 5 t^2 = 5 (2)^2 = 20$.