skan said:how does integral of f(t)*cost dt become and odd function with the integral limit from - pi/2 to pi/2 ?
An odd function is a function in which the value of the function at a negative input is equal to the negative of the value of the function at the corresponding positive input. In other words, if you take the negative of the input and plug it into the function, you will get the same value as you would if you plugged in the positive value. Graphically, an odd function is symmetric about the origin.
An even function is a function in which the value of the function at a negative input is equal to the value of the function at the corresponding positive input. In other words, if you take the negative of the input and plug it into the function, you will get the same value as you would if you plugged in the positive value. Graphically, an even function is symmetric about the y-axis.
To determine if a function is odd or even, you can use the rules for odd and even functions. If the function satisfies the rule for an odd function (f(-x) = -f(x)), then it is an odd function. If the function satisfies the rule for an even function (f(-x) = f(x)), then it is an even function. You can also look at the graph of the function and see if it is symmetric about the origin or the y-axis.
Some examples of odd functions include f(x) = x, f(x) = x^3, and f(x) = sin(x). Some examples of even functions include f(x) = x^2, f(x) = cos(x), and f(x) = |x|.
One property of odd functions is that the integral from -a to a is always equal to 0, where a is any real number. This is because the positive and negative areas of the function cancel each other out. One property of even functions is that the integral from -a to a is always equal to twice the integral from 0 to a. This is because the positive and negative areas of the function are equal and add together to give the total area. Additionally, the product of two odd functions is an even function, and the product of two even functions is an odd function.