9. Find the expression for ∫︁∫︁∫︁∫︁
V
x
l−1y
m−1z
n−1 dx by DZ(Dirichlet’s Integral) in
the form of Gamma integrals, here V is the region x ≥ 0, y ≥ 0, z ≥ 0 and
x + y + z ≤ a.
Hint/Ans: Γ(l)Γ(m)Γ(n)
Γ(l + m + n + 1)
a
l+m+n
10. Evaluate ∫︁
1
1
√
1 − x4
dx
10.
where beta function:
9.
Dirichlet’s Integral:
for gamma function:
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