Question

Solve yzdx + xzdy + xydz = 0

Answer 1

Answer:

I =∫yzdx+xzdy+xydz

where: \IotaI = { I }_{ 1 }I  

1

​

 +{ I }_{ 2 }I  

2

​

 +{ I }_{ 3 }I  

3

​

 

{ I }_{ 1 }I  

1

​

 = \int _{ 0 }^{ 1 }{ yz }∫  

0

1

​

yz dx 0\le x \le 10≤x≤1

={ [ x ] }_{ 0 }^{ 1 }[x]  

0

1

​

 (yz) = (1-0) {yz) =yz

{ I }_{ 2 }I  

2

​

 = \int _{ 0 }^{ 1 }{ xz }∫  

0

1

​

xz dy = 0\le y \le 10≤y≤1

= xz { [ y ] }_{ 0 }^{ 1 }[y]  

0

1

​

 =(xz) (1-0).xz

{ I }_{ 3 }I  

3

​

 = \int _{ 0 }^{ 1 }{ xy }∫  

0

1

​

xy dz = xy { [ z ] }_{ 0 }^{ 1 }[z]  

0

1

​

 0\le z \le 10≤z≤1

= xy (1-0) = xy

\Longrightarrow⟹ \IotaI = { I }_{ 1 }I  

1

​

+{ I }_{ 2 }I  

2

​

+{ I }_{ 3 }I  

3

​

 

\IotaI=yz+xz+xy

Step-by-step explanation: