y=x与xy=1在第三象限的交点是(-1,-1)
所以x的求积范围是(-2,-1)
y的求积范围是(x,1/x)
∫∫x²/y²dxdx
=∫(-2,-1)∫(x,1/x)(x²/y²)dydx
=∫(-2,-1)[-x²/y](x,1/x)dx
=∫(-2,-1)(-x³-(-x))dx
=[(x²/2)-(x^4/4)](-2,-1)
=(1/2-1/4)-(2-4)
=7/4
y=x与xy=1在第三象限的交点是(-1,-1)
所以x的求积范围是(-2,-1)
y的求积范围是(x,1/x)
∫∫x²/y²dxdx
=∫(-2,-1)∫(x,1/x)(x²/y²)dydx
=∫(-2,-1)[-x²/y](x,1/x)dx
=∫(-2,-1)(-x³-(-x))dx
=[(x²/2)-(x^4/4)](-2,-1)
=(1/2-1/4)-(2-4)
=7/4