# Formula for Area of a Triangle - nodal basis function

Let T be a triangle with corners $$P_1, P_2, P_3$$ and the nodal basis function $$\lambda_1, \lambda_2, \lambda_3$$ and $$\alpha, \beta, \in \mathbb{N}_0$$. I want to show that $$\int_{T}^{} \lambda_1^\alpha\lambda_2^\beta \lambda_3^\gamma dx = 2 |T| \frac{\alpha! \beta!\gamma!}{(2+\alpha+\beta+\gamma)}$$ How do I show this and is this a known formula? If so, for what do we need to know and use this?