grandes-ecoles 2023 Q6

grandes-ecoles · France · mines-ponts-maths2__mp Taylor series Limit evaluation using series expansion or exponential asymptotics
Throughout this problem, $I = ]-1, +\infty[$, and $f(x) = \int_0^{\pi/2} (\sin(t))^x \mathrm{~d}t$.
Give a simple asymptotic equivalent of $f(x)$ as $x$ tends to $-1$.
Throughout this problem, $I = ]-1, +\infty[$, and $f(x) = \int_0^{\pi/2} (\sin(t))^x \mathrm{~d}t$.

Give a simple asymptotic equivalent of $f(x)$ as $x$ tends to $-1$.