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How would i determine the t in x and y?
why do you have to \(y = x^2\) \(dy = 2x \, dx\)
It makes sense from that perspective, but i want to replace everything by t.
The book says x=t and y=x^2 |dw:1449787439620:dw|
u can rewrite hte whole thing in t now if uw ant
i just defined a parametric curve
The integration does indeed make sense after know what x(t) and y(t) are. Is this a correct way of solving for x(t) and y(t) ?
well u have x=t then y=t^2 not technically y=t^2 first lol
because this u have 2 solutiosn to x
+/- sqrt t if u dont consider complex
How do yo know we have x=t? Is it because if the information the gave (0,0) to (1,1) ? These two points will give a line after connecting them. Is this the logical way of thinking it?
yeh there is a logical way
u think what vectors will point to every point on my curve
u see that your vectors are of this form some variable in x and that varaible^2 in y
u cudda made your vectors wrt to x too R(x)=
but the bound is wht tells u which of those vectors u are taking
t from o to 1 means u are limited to all those vectors bounding between the points 0,0 to 1,1
For this question: The curve y = sin(πx/2) from (0, 0) to (1, 1) for the same integral.
so basically to get every small tangent vector to this curve u take a small different betwen the positon vectors
then u can apply a function on that small vector
I see what you're saying. Thanks dan :)
might be umm r'(t)
just look at the geometric picture u can figure it out
Makes sense: For this question: The curve x = y^3 from (0, 0) to (1, 1). x(t)=t^3 and y(t)=t|dw:1449790282045:dw|
is it all making sense?