imo class 12 definite integration

Find the value of ∫[0 to 1] x(1 - x)⁹⁹ dx.

VAVidaara Admin Asked 6d ago 0 views 0 answers
#IMO#Class 12#Mathematics#Definite Integration#achievers

Find the value of ∫[0 to 1] x(1 - x)⁹⁹ dx.

  • A. 1/10100
  • B. 1/9900
  • C. 1/100
  • D. 1/10000

Answer: A) 1/10100

Explanation: Using property ∫[0 to 1] f(x) dx = ∫[0 to 1] f(1-x) dx, the integral becomes ∫[0 to 1] (1-x)x⁹⁹ dx = ∫(x⁹⁹ - x¹⁰⁰) dx = [x¹⁰⁰/100 - x¹⁰¹/101] from 0 to 1 = 1/100 - 1/101 = 1/10100.

0 Answers

Log in to post your own answer or join the discussion.

Discussion (0)

No comments yet — start the discussion.

← Back to all questions