Evaluate $$\int_{0}^{c} \int_{x}^{c} e^{x^2+y^2}dydx$$ Given $$\int_{0}^{c}e^{s^2}ds = 3$$ where c is a positive constant.
The solution to this question mentioned that: $$\int_{0}^{c} \int_{x}^{c} e^{x^2+y^2}dydx = \frac{1}{2} \int_{0}^{c} \int_{0}^{c} e^{x^2+y^2}dydx$$ Because the integral in the RHS is evaluated on a triangular region bounded by: $$ y = x \,\,\,\&\,\,\, y = c$$ whereas the one on the LHS is a square region whose area is double the triangular region.
Though I can observe that the region on XY - plane is indeed double, I'm not sure if the relationship would hold while taking a double integral over a non-constant function.