Show that the differential forms in the integrals are exact. Then evaluate the integrals. int_(1,1,2)^(3,5,0)yzdx+xzdy+xydz

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Answered question

2020-11-23

Show that the differential forms in the integrals are exact. Then evaluate the integrals.
1,1,23,5,0yzdx+xzdy+xydz

Answer & Explanation

StrycharzT

StrycharzT

Skilled2020-11-24Added 102 answers

Step 1 
To ascertain: demonstrate the accuracy of the integrals' differential forms. The integrals are then evaluated.
Given: We possess a fundamental 1,1,23,5,0yz dx +xz dy +xy dz  
Explanation:let M = yz, N = xz, P = xy and apply the Test for exactness 
Py=x=Nz 
Mz=y=Px 
Nx=z=My 
It is clear from this that the supplied differential form is accurate. Now, let's think about it
df=yz dx +xz dy +xy dz  for some f, and the integral value is f(3,5,0) -f(1,1,2) 
Step 2 
1,1,23,5,0yz dx +xz dy +xy dz =[yzx+xzy+xyz]1,1,23,5,0 
=[3xyz]1,1,23,5,0 
=3[(3×5×0)(1×1×2)]=6

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-05Added 2605 answers

Answer is given below (on video)

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