Evaluate ∫₀¹ x (1 − x)⁹ dx.

Evaluate ∫₀¹ x (1 − x)⁹ dx.

• A. 1/110
• B. 1/90
• C. 1/132
• D. 1/100

Answer: A) 1/110

Explanation: Beta function: ∫₀¹ x^(m−1) (1−x)^(n−1) dx = B(m,n) = Γ(m)Γ(n)/Γ(m+n). Here x = x¹ so m−1=1 → m=2. (1−x)⁹ so n−1=9 → n=10. B(2,10) = Γ(2)Γ(10)/Γ(12) = 1! 9! / 11! = 1/(10×11) = 1/110.