An even function is a mathematical function that has symmetry about the y-axis. This means that if you reflect the graph of the function over the y-axis, it will look exactly the same.
The integral of an even function is the area under the curve from the negative x-axis to the positive x-axis. This can be calculated using the definite integral or by finding the antiderivative of the even function.
A function is even if it satisfies the condition f(-x) = f(x) for all values of x. This means that the output of the function at a negative value of x is the same as the output at the corresponding positive value of x.
Yes, all even functions are symmetric about the y-axis. This is because the definition of an even function includes the condition of symmetry about the y-axis.
One example of an even function is f(x) = x2. Its integral would be F(x) = (1/3)x3 + C.