Daily math problems for July 5, 2026 — Algebra, Integrals, Financial Mathematics

Group axioms: associativity, identity element, every element has an inverse. Commutativity is the additional axiom for an abelian group.

$\bullet$ Simplify the integrand:

$$\frac{\sqrt[7]{x^3}}{x^2}=\frac{x^{3\mathrm{/}7}}{x^2}=x^{-11\mathrm{/}7}$$

$\bullet$ The integral ${\int }_0^a{x}^{p}dx$ converges only when $p>-1$:

$$-\frac{11}{7}<-1$$

$\bullet$ Hence the integral diverges at the lower endpoint $x=0$:

$${\int }_0^{10}{x}^{-11\mathrm{/}7}dx=\text{Diverges}$$

After both moves, the value is $0.8\cdot 1.2=0.96$ — a $4\mathrm{\%}$ net loss.