# Thread: another question on line integral

1. ## another question on line integral

another question on line integral
i have to evaluate the line integral
∫c (xy)^2 dx + xy^2 dy
where c is closed curve formed by x=1 and y^2=x

for this question. i drew a diagram which has three sides.
c1 : x=1, y=t, 0<t<1
c2 : x=t, y=0, 0<t<1
c3 : x=t , y=x^1/2 , 0<t<1

the book says the answer is 4/15. but i keep getting wrong answers
where did i make mistake??

2. Originally Posted by panda
another question on line integral
i have to evaluate the line integral
∫c (xy)^2 dx + xy^2 dy
where c is closed curve formed by x=1 and y^2=x

for this question. i drew a diagram which has three sides.
c1 : x=1, y=t, 0<t<1
c2 : x=t, y=0, 0<t<1
c3 : x=t , y=x^1/2 , 0<t<1

the book says the answer is 4/15. but i keep getting wrong answers
where did i make mistake??
Just post what you did thus we can show the error.

3. i just integrated each of them
then i got
c1= 1/3
c2=0
c3=9/20

and then if i add them all together, i get 47/60 which is different to the answer given in the book.

the parametric set that I've written(c1,c2 and c3)..did i do it right?