4.62 Double and triple integrals with constant limits

4.620 General formulas

1. 

0πdω?0f?(p?cosh?x+q?cos?ω?sinh?x)?sinh?x?dx?=π?sign?pp2q2f(sign?pp2q2)

si1483_e  LO III 389

[p2>q2,limx+f(x)=0]si1484_e

2. 

02πdω0f[p?cosh?x+(q?cos?ω+r?sin?ω)?sinh?x]?sinh?x?dx=2π?sign?pp2q2r2f(signpp2q2r2)

si1485_e  LO III 390

[??p2>q2+r2,limx+f(x)=0]si1486_e

3. 

0π0πdx?dy

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