grandes-ecoles 2011 Q15

grandes-ecoles · France · centrale-maths1__pc Indefinite & Definite Integrals Definite Integral Evaluation (Computational)
We consider a rectangle $]a,b[ \times ]c,d[$ of the plane $\mathbb{R}^{2}$, with $a < b$ and $c < d$. Calculate the real number $V(]a,b[ \times ]c,d[)$. What does it represent? (One may use functions of the type $$(x,y) \mapsto f(x,y) = \phi(x)\varphi(y)$$ where $\phi$ and $\varphi$ are well-chosen continuous and piecewise affine functions).
We consider a rectangle $]a,b[ \times ]c,d[$ of the plane $\mathbb{R}^{2}$, with $a < b$ and $c < d$. Calculate the real number $V(]a,b[ \times ]c,d[)$. What does it represent? (One may use functions of the type
$$(x,y) \mapsto f(x,y) = \phi(x)\varphi(y)$$
where $\phi$ and $\varphi$ are well-chosen continuous and piecewise affine functions).