find ∫G(x,y)ds ??? , on the indicated curve
G(X,Y)=2XY, C: X=5*COST, Y=5*SINT,
0≤t≤π÷4

Question

find ∫G(x,y)ds ??? , on the indicated curve 
G(X,Y)=2XY, C: X=5*COST, Y=5*SINT, 
0≤t≤π÷4

akshay_budhkar · Answer

ok i will give u a hint, u should solve it yourself :D

anonymous · Answer

ok no problem

akshay_budhkar · Answer

$$2 \sin(x) \cos(x)=\sin(2x)$$

akshay_budhkar · Answer

so your G(x,y) =

akshay_budhkar · Answer

$$2 \times 5 \times \cos(x) \times 5 \times \sin(x)$$

akshay_budhkar · Answer

= $$25 \sin (2x)$$

akshay_budhkar · Answer

you can intergerate that :D

anonymous · Answer

i know how to find $$\int\limits_{C}^{} G(x,y) dx $$ and $$\int\limits_{C}^{} G(x,y) dy $$ what i want is $$\int\limits_{C}^{} G(x,y) ds $$

akshay_budhkar · Answer

one min i need to get a better help 1 second

anonymous · Answer

i am thinking that i should add $$\int\limits_{C}^{} G(x,y) dx + \int\limits_{C}^{} G(x,y) dy  $$  but i am not sure

akshay_budhkar · Answer

@turing ds???

anonymous · Answer

what do you think ?

turingtest · Answer

I'm sorry I'm multitasking...

anonymous · Answer

this is how the question written exactly ... what does he mean by ds?

akshay_budhkar · Answer

i don't know that is why i called turing

akshay_budhkar · Answer

ds? are u sure that is what is asking for?

anonymous · Answer

yes i am sure

anonymous · Answer

the answer will be 125/2 .. but i do not know how to get it

akshay_budhkar · Answer

why do you think you need to add?

akshay_budhkar · Answer

ds generally in my questions is the area

anonymous · Answer

really i am not sure i tried everything but i could not reach the answer

akshay_budhkar · Answer

i am waiting for turing to respond lol.. he will surely help.. i m thinking of possibilities till then

anonymous · Answer

ok I appreciate your help bro .. thanks.

akshay_budhkar · Answer

no no its not done! i wont sleep till u get ur answer :P

anonymous · Answer

Lol thanks so much.. me too cuz i have to submit this assignment  tomorrow :D

turingtest · Answer

ok 
ds=sqrt[(dx/dt)^2+(dy/dt)^2]=5
2xy=50cost*sint
got it from there?

anonymous · Answer

Integrating with respect to ds means that you are integrating with respect to the arc length (which is often denoted s) of the curve C. Note that $$ds=\sqrt{dx^2+dy^2}=\sqrt{(-5\cos (t) dt)^2+(5\sin (t) dt)^2}=5dt$$ Thus, you have that $$\int_C G(x,y)ds=\int_0^{\pi/4}25\sin(2t)\cdot 5dt = \int_0^{\pi/4}125\sin(2t)dt = \frac{125}{2}$$

akshay_budhkar · Answer

ds?

akshay_budhkar · Answer

arc length is what it signifies?

turingtest · Answer

yes, you need ds in line integrals, arc length differential

anonymous · Answer

thanks guys I get it .. I appreciate your help .