Zela101
  • Zela101
Evaluate the integral: The parabolic arc y=x^2 from (0,0) to (1,1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Zela101
  • Zela101
\[\int\limits_{c}^{}(3x+2y)dx+(2x-y)dy\]
Zela101
  • Zela101
How would i determine the t in x and y?
IrishBoy123
  • IrishBoy123
why do you have to \(y = x^2\) \(dy = 2x \, dx\)

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More answers

IrishBoy123
  • IrishBoy123
\[\int\limits_{c}^{}(3x+2x^2)dx+(2x-x^2)2x dx\]
Zela101
  • Zela101
It makes sense from that perspective, but i want to replace everything by t.
Zela101
  • Zela101
@dan815
Zela101
  • Zela101
The book says x=t and y=x^2 |dw:1449787439620:dw|
dan815
  • dan815
|dw:1449787436815:dw|
dan815
  • dan815
x=t y=t^2
dan815
  • dan815
u can rewrite hte whole thing in t now if uw ant
Zela101
  • Zela101
How come?
dan815
  • dan815
i just defined a parametric curve
dan815
  • dan815
|dw:14497875|dw:1449787563831:dw|9743:dw|
Zela101
  • Zela101
|dw:1449787580028:dw|
dan815
  • dan815
|dw:1449787610119:dw|
dan815
  • dan815
|dw:1449787856168:dw|
Zela101
  • Zela101
|dw:1449787965037:dw|
Zela101
  • Zela101
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) ?
dan815
  • dan815
well u have x=t then y=t^2 not technically y=t^2 first lol
dan815
  • dan815
because this u have 2 solutiosn to x
dan815
  • dan815
+/- sqrt t if u dont consider complex
Zela101
  • Zela101
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?
Zela101
  • Zela101
|dw:1449788218785:dw|
dan815
  • dan815
yeh there is a logical way
dan815
  • dan815
u think what vectors will point to every point on my curve
dan815
  • dan815
|dw:1449789421074:dw|
dan815
  • dan815
u see that your vectors are of this form some variable in x and that varaible^2 in y
dan815
  • dan815
u cudda made your vectors wrt to x too R(x)=
dan815
  • dan815
but the bound is wht tells u which of those vectors u are taking
dan815
  • dan815
t from o to 1 means u are limited to all those vectors bounding between the points 0,0 to 1,1
Zela101
  • Zela101
For this question: The curve y = sin(πx/2) from (0, 0) to (1, 1) for the same integral.
Zela101
  • Zela101
|dw:1449789804404:dw|
Zela101
  • Zela101
|dw:1449789904505:dw|
dan815
  • dan815
|dw:1449789909464:dw|
dan815
  • dan815
|dw:1449789934744:dw|
Zela101
  • Zela101
Yes.
dan815
  • dan815
so basically to get every small tangent vector to this curve u take a small different betwen the positon vectors
dan815
  • dan815
then u can apply a function on that small vector
Zela101
  • Zela101
|dw:1449790099383:dw|
dan815
  • dan815
|dw:1449790057995:dw|
Zela101
  • Zela101
I see what you're saying. Thanks dan :)
dan815
  • dan815
might be umm r'(t)
dan815
  • dan815
just look at the geometric picture u can figure it out
Zela101
  • Zela101
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|
Zela101
  • Zela101
THANK YOUUUU
dan815
  • dan815
|dw:1449790231663:dw|
dan815
  • dan815
|dw:1449790671706:dw|
dan815
  • dan815
|dw:1449791044895:dw|
dan815
  • dan815
|dw:1449791088129:dw|
dan815
  • dan815
is it all making sense?
Zela101
  • Zela101
Yes
Zela101
  • Zela101
Thanks :D

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