anonymous
  • anonymous
find ∫G(x,y)ds ??? , on the indicated curve G(X,Y)=2XY, C: X=5*COST, Y=5*SINT, 0≤t≤π÷4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Akshay_Budhkar
  • Akshay_Budhkar
ok i will give u a hint, u should solve it yourself :D
anonymous
  • anonymous
ok no problem
Akshay_Budhkar
  • Akshay_Budhkar
\[2 \sin(x) \cos(x)=\sin(2x)\]

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Akshay_Budhkar
  • Akshay_Budhkar
so your G(x,y) =
Akshay_Budhkar
  • Akshay_Budhkar
\[2 \times 5 \times \cos(x) \times 5 \times \sin(x)\]
Akshay_Budhkar
  • Akshay_Budhkar
= \[25 \sin (2x)\]
Akshay_Budhkar
  • Akshay_Budhkar
you can intergerate that :D
anonymous
  • anonymous
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
  • Akshay_Budhkar
one min i need to get a better help 1 second
anonymous
  • anonymous
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
  • Akshay_Budhkar
@turing ds???
anonymous
  • anonymous
what do you think ?
TuringTest
  • TuringTest
I'm sorry I'm multitasking...
anonymous
  • anonymous
this is how the question written exactly ... what does he mean by ds?
Akshay_Budhkar
  • Akshay_Budhkar
i don't know that is why i called turing
Akshay_Budhkar
  • Akshay_Budhkar
ds? are u sure that is what is asking for?
anonymous
  • anonymous
yes i am sure
anonymous
  • anonymous
the answer will be 125/2 .. but i do not know how to get it
Akshay_Budhkar
  • Akshay_Budhkar
why do you think you need to add?
Akshay_Budhkar
  • Akshay_Budhkar
ds generally in my questions is the area
anonymous
  • anonymous
really i am not sure i tried everything but i could not reach the answer
Akshay_Budhkar
  • Akshay_Budhkar
i am waiting for turing to respond lol.. he will surely help.. i m thinking of possibilities till then
anonymous
  • anonymous
ok I appreciate your help bro .. thanks.
Akshay_Budhkar
  • Akshay_Budhkar
no no its not done! i wont sleep till u get ur answer :P
anonymous
  • anonymous
Lol thanks so much.. me too cuz i have to submit this assignment tomorrow :D
TuringTest
  • TuringTest
ok ds=sqrt[(dx/dt)^2+(dy/dt)^2]=5 2xy=50cost*sint got it from there?
anonymous
  • anonymous
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
  • Akshay_Budhkar
ds?
Akshay_Budhkar
  • Akshay_Budhkar
arc length is what it signifies?
TuringTest
  • TuringTest
yes, you need ds in line integrals, arc length differential
anonymous
  • anonymous
thanks guys I get it .. I appreciate your help .

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