- #1
NewtonianAlch
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Homework Statement
[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
Homework Equations
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?