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 March 13th, 2014, 03:01 PM #1 Senior Member   Joined: Apr 2008 Posts: 193 Thanks: 3 Is this question solvable? If f(x) is symmetric about the origin and $\int_{0}^{2}f(x)dx$ = a, find $\int_{-2}^{2}f(x)dx$. my attempt $\int_{-2}^{2}f(x)dx$ = $\int_{-2}^0f(x)dx$ + $\int_0^{2}f(x)dx$ = a + $\int_0^{2}f(x)dx$ Can someone please explain whether it is possible to evaluate the last integral? Thanks.
 March 13th, 2014, 07:05 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Is this question solvable? Seriously? That last integral is exactly the one you are told is equal to a! The first one is NOT equal to a because you are told the function is "symmetric about the origin". What does that mean?
 March 13th, 2014, 07:06 PM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Is this question solvable? Accidental double post.
 March 13th, 2014, 11:10 PM #4 Senior Member   Joined: Mar 2014 Posts: 112 Thanks: 8 Well since it's symmetric it's obviously 2a.
March 14th, 2014, 06:37 AM   #5
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Re:

Quote:
 Originally Posted by the john Well since it's symmetric it's obviously 2a.
That would be correct if it were "symmetric about the y-axis".

But this problem says the function is "symmetric about the origin". That is, f(-x)= -f(x).

The integral from -2 to 2 is 0.

 March 22nd, 2014, 11:04 PM #6 Senior Member   Joined: Mar 2014 Posts: 112 Thanks: 8 My above post gives an example of f(x) = x², where your correct explanation gives f(x) = x³ as an example.
 March 23rd, 2014, 06:12 AM #7 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Is this question solvable? Yes, $f(x)= x^2$ is "symmetric about the y-axis" while $g(x)= x^3$ is "symmetric about the origin".

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