A collection of mathematical exercises focusing on integrals, inequalities, and their proofs.
Extract
[...] Suites of Integrals Exercises: I° II° Exercise Let's transform the following integral by performing a partial integration: and are on . One obtains: For belonging to the interval , on a : Thus, we get: The right-hand side of the inequality tends towards when tend towards , on deduces that tend also to when tend to . On Thus, according to the previous question: is therefore equivalent to Exercise On The last line comes from the fact that Let's The inequality found in then gives us: When dividing by (If both members of this inequality are strictly positive, then the inequality of the statement is obtained. [...]
