If R=[0,1]x [0,1], show that 0le int int_R sin(x+y)dA le 1

skilpadw3 2022-08-01 Answered
If R=[0,1]x [0,1], show that 0 R sin ( x + y ) d A 1
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Answers (1)

phravincegrln2
Answered 2022-08-02 Author has 19 answers
If R = [0, 1] x [0, 1], show that 0 R sin ( x + y ) d A 1
the region R = ( ( x , y ) | 0 x 1 , 0 y 1 )
therefore the integral becomes.
0 1 0 1 sin ( x + y ) d x d y
= 0 1 [ cos ( x + y ) ] 0 1 d y
= 0 1 [ cos ( 1 + y ) cos ( y ) ] d y
= [ sin ( 1 + y ) sin ( y ) ] 0 1
= [ ( sin 2 sin 1 ) ( sin 1 sin 0 ) ]
= 2 sin 1 sin 2 0.774
0 0.774 1
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