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xdrgnh
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Is the integral of an even function an odd function and vice versa? I know the derivative is.
Thats your loss then. It would do you good.xdrgnh said:I'm a physics major who needs to calculate a Fourier series for a driven oscillator I got no time to prove it. But thanks anyway.
An odd function is a mathematical function that satisfies the property f(-x) = -f(x). This means that when the input of the function is multiplied by -1, the output is equal to the negative of the original output. Graphically, an odd function has symmetry about the origin.
An even function is a mathematical function that satisfies the property f(-x) = f(x). This means that when the input of the function is multiplied by -1, the output remains the same. Graphically, an even function has symmetry about the y-axis.
The integral of an odd function over a symmetric interval is equal to 0. This is because the positive and negative areas of the function cancel each other out, resulting in a net area of 0. This property is known as the odd function integral property.
The integral of an even function over a symmetric interval is equal to twice the integral of the function over one half of the interval. This is because the positive and negative areas of the function are equal, so they can be combined to find the total area. This property is known as the even function integral property.
Yes, an odd or even function can have a non-zero integral over a non-symmetric interval. This is because the symmetry property only applies to symmetric intervals. When the interval is not symmetric, the positive and negative areas of the function do not cancel each other out.