(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]\int[/itex] (1 - x^2)^n dx = [itex]\frac{2n}{2n+1}[/itex] [itex]\int[/itex] (1 - x^2)^n-1 dx

for n greater or equal to 1, find [itex]\int[/itex] (1 - x^2)^4 dx

The integrals go from 0 to 1

2. Relevant equations

3. The attempt at a solution

Well what I did was to keep doing n - 1 whilst pulling a fraction outside the integral and multiplying each subsequent fraction.

So I ended up with 8/9 * 6/7 * 4/5 and the integral of (1 - x) which became x - x^2/2

Substituting in 1 and 0, subtracting and the multiplying by the fractions I got 192/305*1/2 which simplifies to 96/305.

Is this the correct procedure for evaluating reduction formulae, and was my answer correct?

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# Evaluation of a reduction formula

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