Double integration by using Gamma function, Exams of Mathematics

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TT a Calculate: { sin(x + y)sin(x — y)dydx o Jo ron 2 Solution: i i o /o z 2 z z ih sin?x f cos’y dy ax—| cos?x [ sin?y dy| dx 0 0 0 0 T 1 3 1 2 rhs, {* ) = adr) _ 208 : zi AT (Qe ODF a a 1 3 1 z Fa gy t/t 3\_ Pla)E (a) _ 30%) so, | sin ydy=>B = —or2) SCO 2 Te 2 sin’xcos? ydydx — cos’ xsin? ydydx ia oa rs 4 rs 4 Te Te Tt Tr Zz z 2 [2 cos*y dy = | sin’ydy => { [ sin(x + y)sin(x — y)dydx = 0 0 0 o Jo MR. OSAMA A.A. ALSATTARI since |