Find the average value of f over the given rectangle. f(x,y)=x^2y,

tricotasu

tricotasu

Answered question

2021-10-18

Find the average value of f over the given rectangle.
f(x,y)=x2y,
R has vertices (-1,0), (-1,5), (1,5), (1,0)

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-10-19Added 94 answers

Average value of f=1ARf(x,y)dA
R=[1,1]×[0,5]
A=25=10
Average value of f=11011[05x2y dy ] dx 
x = constant
=11011[12x2(5)2 dx  
=11011252x2 dx 
=5411x2 dx 
=54[x33]11
=54[133(1)33]
=54[23]=56
Answer: 56

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