Question

double integration of xy limit y=x,y²=2x,x²+y²-2x=0​

Answer 1

Answer:

I would do this way:

x2 + y2=2x

(x-1)2 + y2=1

Then x = 1+ rcosθ, y = rsinθ; dxdy = rdrdθ and x2 + y2 = (1+ rcosθ)2+sin2θ =1+r2+2rcosθ.

D= {(r, θ): 0≤r≤1, 0≤θ≤2π}

Then

∫∫D(x2 + y2)dxdy=∫∫D(r + r3 +2r2cosθ) drdθ = 3π / 2,

Step-by-step explanation:

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Answer 2

Answer:

$xy,\:y=x,\:y^2=2x,\:x^2+y^2-2x=0:\quad x^2$

Step-by-step explanation:

$\mathrm{Find\:}xy\:\mathrm{given}\:y=x,\:y^2\left(x\right)=2x,\:x^2+y^2-2x=0$

$y=x$

$xx=\:x^{1+1}$

$=x^{1+1}$

=x²