Line integrals help

[thedudeadrian]

Hi I'm working with line integrals and when I'm calculating |r'(t)| of x=t and y=t² I get sqrt(1²+(2t)²). This is equal to = 1 + 4t². But my book tells me that the answer is 2t which makes no sense at all.

Im doing task 6 on the tasks on the picture I added.

Thanks,
Adrian

 

[Steven G]

Please share your work with us so we can see if you made any errors and/or if the solution is wrong.

 

[thedudeadrian]

My answer: But correction says to use 2t instead of sqrt(1+4t²)



This is the correct solution below. I don't understand how they get 2t instead sqrt(1+4t²).

 

[LCKurtz]

Hi I'm working with line integrals and when I'm calculating |r'(t)| of x=t and y=t² I get sqrt(1²+(2t)²). This is equal to = 1 + 4t². But my book tells me that the answer is 2t which makes no sense at all.

Im doing task 6 on the tasks on the picture I added.

Thanks,
Adrian

Unfortunately, your picture cut off the statement of the first part of the problem. That might not seem relevant to you but I suspect your difficulty is related to it. I'm guessing the integrals in 1 - 5 are integrals with respect to arc length like [MATH]\int_C f(x,y)~ds[/MATH]. That is why you are wanting to calculate [MATH]ds = \sqrt{1 + y'^2}~dx[/MATH]. Problem 6 and the others are ordinary line integrals, not arc length type. I think this assignment is to help you see the difference and how to work them.