Let $f:\mathbb{R}^2\rightarrow\mathbb{R}$ be a smooth function (derivable, integrable over all of $\mathbb{R}^2$). Let $T$ be a triangle in $\mathbb{R}^2$, defined by its vertices : $A=(x_a,y_a)$, $B=(x_b,y_b)$, $C=(x_c,y_c)$. Let $I$ be the integral of $f$ over $T$ : $$ I = \iint_T f(x,y)dxdy$$ Is there a generic formula for $I$ based on $f$, $x_a,y_a$, $x_b,y_b$, $x_c,y_c$ ?
EDIT : In my case, $f(x,y)=cos(x)$