- #1
LagrangeEuler
- 717
- 20
If function is ##f(-x,-y)=f(x,y)##, is then
##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=0##?
Thanks for answer.
##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=0##?
Thanks for answer.
LagrangeEuler said:Could you tell me some explanation why this is valid only for one integral?
LagrangeEuler said:If function is ##f(-x,-y)=f(x,y)##, is then
##\int^{a}_{-a}\int^{a}_{-a}f(x,y)dxdy=0##?
Thanks for answer.
An integral having symmetry means that the value of the integral is the same regardless of the direction in which it is integrated. In other words, if the limits of integration are reversed, the value of the integral remains unchanged.
To determine if an integral is symmetric, you can use the substitution method. If after substituting -x for x in the integrand, the integrand remains unchanged, then the integral is symmetric.
An integral being symmetric is significant because it allows us to simplify the integration process. By taking advantage of symmetry, we can reduce the number of integrals we need to solve and make the problem more manageable.
Yes, an integral can still be symmetric even if the limits of integration are not symmetric. As long as the integrand remains unchanged after substituting -x for x, the integral is considered symmetric.
No, the value of a symmetric integral is not always zero. While some symmetric integrals may evaluate to zero, others may not. It ultimately depends on the integrand and the limits of integration.