Evaluate the triple integral E xydV, where is bounded by the parabolic cylinders

Clifland

Clifland

Answered question

2021-10-08

Evaluate the triple integral E xydV, where the parabolic cylinders define the boundaryy=x2  and  x=y2 and the planes z=0 and z=x+y

Answer & Explanation

davonliefI

davonliefI

Skilled2021-10-09Added 79 answers

The solid is provided above the area that is enclosed by two parabolas that intersect at a particular point (1,1) given with the equations x=y2  and  y=x2. Expressing y from the first equation yields us the following triple integral: 
01x2x0x+yxy dz  dy  dx =01x2xx2y+xy2 dy  dx  
Next we calculate the remaining double integral: 
01x2xx2y+xy2 dy  dx =013x3+2x53x62x76 dx =328 
Results: 
328

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