Asked by Jamie
Write the following function as the sum of an odd and an even function. Then calculate the integral over the given interval using the properties of odd and even functions.
(x-1)^3, I=[-1,1]
(x-1)^3, I=[-1,1]
Answers
Answered by
Anonymous
x(x^2-2x+1)
-1(x^2-2x+1)
= x^3 - 2x^2 + x - x^2 + 2x - 1
= (x^3 + 3x)odd ( -3x^2 -1) even
the odd part will give zero (+ on one side of x = 0 and - on the other)
so
-x^3 - x = - (x^3+x)so (x^3+x) at -1 - at +1
-1-1 - 1-1 = -4
-1(x^2-2x+1)
= x^3 - 2x^2 + x - x^2 + 2x - 1
= (x^3 + 3x)odd ( -3x^2 -1) even
the odd part will give zero (+ on one side of x = 0 and - on the other)
so
-x^3 - x = - (x^3+x)so (x^3+x) at -1 - at +1
-1-1 - 1-1 = -4
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