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Wislar
 3 years ago
Please Check!
Line integral: \[\int\limits_{C}^{}x ^{2}dx+y ^{2}dy\] of the line segment from (0,2) to (4,3)
Wislar
 3 years ago
Please Check! Line integral: \[\int\limits_{C}^{}x ^{2}dx+y ^{2}dy\] of the line segment from (0,2) to (4,3)

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Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0Is it: \[\int\limits_{0}^{4}16t ^{2}(4)+(2+t)^{2}(1)dt\]

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0The parameterized curve is r(t)=(4t, 2+t) right?

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0@phi @amistre64 @Zarkon @TuringTest

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1id have a little reading to do to catch up on this :)

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0I think I have it down correctly, I'm just not sure if the limit is from 0 to 4

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1we need to parametrize the line from 0,2 to 4,3 right?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.14,3 02  <4,1> is the direction vector, and we can apply it to either point given so one parametric could be: x = 0 + 4t y = 2 + t

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0That's what I got! I'm not sure about the limits of integration though

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1the dx and dy parts in your post got me confuddled. im used to seeing a ds in it

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1here we go http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtII.aspx

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1\[\int_CPdx+Qdy=\int_CPdx+\int_CQdy\]

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1x = 0 + 4t dx = 4 dt y = 2 + t dy = dt

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0I have that down @amistre64 I'm just really not sure about the limits. I just used the x coordinates.

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1what are the limits of t for the given line?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1when t=0 we are at (0,2) when t=? we are at (4,3)

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.10 = 0 + 4t 2 = 2 + t t=0 4 = 0 + 4t 3 = 2 + t t = 1 so the limit of our t is 0 to 1

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0Wait how did you do that?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1we are changing x and y into functions of t correct?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1then "with respect to t" the line is from t=0 to t=1 since (0,2) is t=0; and (4,3) is t=1

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1we are simply defining all the terms with respect to t; x,y and movement

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0I have another question that asks for the line integral that consists of the arc of the circle x^2+y^2=4 from (2,0 to (0,2) I know how to find the line integral, but the limits are what I'm not sure about again

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0The parameterized curve is (2cost,2sint)

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1is it asking you to define it by the line that goes from 2,0 to 0,2? or from the arc that goes from 2,0 to 0,2 ?

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0It says the arc of the circle from (2,0) to (0,2)

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1x = r cos(t) y = r sin(t) and from the equation r = 2 x = 2 cos(t) dx = 2sin(t) y = 2 sin(t) dy = 2 cos(t) what is the value of t for the point x=2, y=0? what is the value of t for the point x=0, y=2?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.12 = 2 cos(t) 0 = 2 sin(t) cos(t) = 1 and sin(t) = 0 when t = 0 0 = 2 cos(t) 2 = 2 sin(t) cos(t) = 0 and sin(t) = 1 when t = pi/2

Wislar
 3 years ago
Best ResponseYou've already chosen the best response.0So it's from 0 to pi/2 right?

amistre64
 3 years ago
Best ResponseYou've already chosen the best response.1youre welcome, and good luck :)
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