grandes-ecoles 2024 Q9

grandes-ecoles · France · mines-ponts-maths2__psi Integration using inverse trig and hyperbolic functions

Consider the function $h : ]0,1[ \longrightarrow \mathbf{R},\; t \longmapsto \frac{1}{\sqrt{t(1-t)}}$. Show that: $$\int_0^1 h(t)\, dt = \pi.$$

Consider the function $h : ]0,1[ \longrightarrow \mathbf{R},\; t \longmapsto \frac{1}{\sqrt{t(1-t)}}$. Show that:
$$\int_0^1 h(t)\, dt = \pi.$$