Question

Even & Odd properties problem

Answer 1

\[\int\limits_{-2}^{2} x ^{2} (x^{2}+1) DX\]

Answer 2

Hey again John

Answer 3

Hey Kuggy, had this problem come up and do not remember the properties at all

Answer 4

So for this one, because the powers are positive, f(x) will be symmetric over the y-axis,
Therefore int[-2,2]f(x)dx = 2int[0,2]f(x)dx

Answer 5

So like, its a parabolic f(x), so itll be symmetrical over the y-axis... thats for EVEN powers.. even parabolas haha

Answer 6

for Odd powers, the graph will be symmetric over the line y=x, which pretty much just means the integral of f(-x) is the same as - integral f(x)

Answer 7

\[2 \int\limits_{0}^{2} f(x)DX\]

Answer 8

im not sure i follow

Answer 9

@Kuggy

Answer 10

yeah that is right

Answer 11

because like [-2,0] and [0,2] are the exact same amount when you do that integral, so you can just do from [0,2] and multiply by 2

Answer 12

A walkthrough would be nice please