Calculate the double integral int int (6x)/(1+xy)dA, R=[0,6]x[0,1]

armlanna1sK

armlanna1sK

Answered question

2022-11-26

Calculate the double integral.
6 x 1 + x y d A ,   R = [ 0 , 6 ] × [ 0 , 1 ]

Answer & Explanation

cute4life1404i7N

cute4life1404i7N

Beginner2022-11-27Added 11 answers

Given that the function to be integrated is:
f ( x , y ) = 6 x 1 + x y
Over region R = [ 0 , 6 ] × [ 0 , 1 ]
i.e, x from 0 to 6
y from 0 to 1
Definite integral is
R f ( x , y ) d A = x = 0 x = 6 y = 0 1 6 x 1 + x y d y d x = x = 0 x = 6 6 x ln | 1 + x y | x | y = 0 y = 1 d x = x = 0 x = 6 ( 6 ln | 1 + x | 6 ln | 1 + 0 | ) d x = x = 0 x = 6 6 ln | 1 + x | d x = 6 x = 0 x = 6 ln | 1 + x | d x = 6 ( 7 ln ( 7 ) 6 ) = 42 ln ( 7 ) 46 = 45.728

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