2°) Use integration by parts to prove that, for any positive integer n, (2n + 1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n. (n!)2 In (2n + 1)!"

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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i really just need help with 2 and 3

Let In =
| (1- t2)" dt, for any nonnegative integer n.
1°)
Calculate Io and I1.
2°)
Use integration by parts to prove that, for any positive integer n,
(2n +1) In = 2n In-1.
3°)
Show that, for any nonnegative integer n,
22n . (n!)2
In
(2n + 1)!
%3D
Transcribed Image Text:Let In = | (1- t2)" dt, for any nonnegative integer n. 1°) Calculate Io and I1. 2°) Use integration by parts to prove that, for any positive integer n, (2n +1) In = 2n In-1. 3°) Show that, for any nonnegative integer n, 22n . (n!)2 In (2n + 1)! %3D
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