grandes-ecoles 2023 Q8

grandes-ecoles · France · mines-ponts-maths2__mp Curve Sketching Sketching a Curve from Analytical Properties
Throughout this problem, $I = ]-1, +\infty[$, and $f(x) = \int_0^{\pi/2} (\sin(t))^x \mathrm{~d}t$.
Sketch the graph of $f$ by making best use of the previous results.
Throughout this problem, $I = ]-1, +\infty[$, and $f(x) = \int_0^{\pi/2} (\sin(t))^x \mathrm{~d}t$.

Sketch the graph of $f$ by making best use of the previous results.