plz make one video about different type of integrals and when we use it. plz relate integrals from cal 1 to cal 3. like line integrals and surface integ and so on.
Thanks, David! I actually figured this out like five minutes after I asked haha. Although, my university doesn't do t-subs for some reason. I had never seen this before. o_O
The parameterization can be anything that satisfies y = x^2. Let's say we choose x = t and y = t^2. The original curve satisfies y = x^2, but we let x = t, so then y = t^2, so this parameterization is valid. If we chose, as you said, x = t^2 and y = t, then y ≠ x^2 as t ≠ (t^2)^2. Instead, we would instead need to choose y = t^4 as y = x^2 = (t^2)^2 = t^4. This would also be valid. In general, if we have some function y = f(x), then we can always paramaterize it as x = t, y = f(t).
@@DavidStojanovski I know I am commenting on this 8 years after the fact, but it can be almost anything where y = x^2. It can depend also on the points where you start and end. For example, if we look at the curve y = x^2 from (-1,1) to (2,4), we cannot use the parameterization x = t^2 and y = t^4 even though y = x^2 in this parameterization. That is because in this parameterization, x is nonnegative and so the part of the curve from (-1,1) up to (0,0) would not be covered by this parameterization.
Didnt he forget the notation for the line integral? Shouldnt it be the integram with a circle through it? Anyway doesnt matter im just curious. This guy is amazing.
If the path is a closed path (such as a circular path) then you put the circle. Here, Joel considers a regular curve with two independent ends.
Yeah, the circle is for a closed path, as seen in physics a lot. Ampere's law, etc.
plz make one video about different type of integrals and when we use it. plz relate integrals from cal 1 to cal 3. like line integrals and surface integ and so on.
Thanks, David! I actually figured this out like five minutes after I asked haha. Although, my university doesn't do t-subs for some reason. I had never seen this before. o_O
Muchas gracias, muy claro...
Where do x=t and y=t^2 come from? don't those generally come from the curve parameters? why wouldnt it be x=t^2 and y=t?
and t*t^2 = t^3.... where is that 3 in the front coming from?
The parameterization can be anything that satisfies y = x^2. Let's say we choose x = t and y = t^2. The original curve satisfies y = x^2, but we let x = t, so then y = t^2, so this parameterization is valid. If we chose, as you said, x = t^2 and y = t, then y ≠ x^2 as t ≠ (t^2)^2. Instead, we would instead need to choose y = t^4 as y = x^2 = (t^2)^2 = t^4. This would also be valid. In general, if we have some function y = f(x), then we can always paramaterize it as x = t, y = f(t).
@@DavidStojanovski I know I am commenting on this 8 years after the fact, but it can be almost anything where y = x^2. It can depend also on the points where you start and end. For example, if we look at the curve y = x^2 from (-1,1) to (2,4), we cannot use the parameterization x = t^2 and y = t^4 even though y = x^2 in this parameterization. That is because in this parameterization, x is nonnegative and so the part of the curve from (-1,1) up to (0,0) would not be covered by this parameterization.
@@MetroidMann Good point, Thanks for pointing this out. Parameterization should be invertible or bijective i.e. there should be one-to-one mapping.
thank you very much!
thank you very much.. you really Good
thanks seinfeld
When he takes the derivative of x2+y2 it should be 2y which should be 2t^2 not 2t
review your derivatives buddy
Didnt he forget the notation for the line integral? Shouldnt it be the integram with a circle through it? Anyway doesnt matter im just curious. This guy is amazing.
You only put a circle on the integral symbol if you're integrating along a closed (usually simple) curve
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