Daily math problems for September 30, 2026 — Absolute value, Calculus, Logic & more

The sum of all real solutions of $\mathrm{\mid }x-3\mathrm{\mid }=5$ is:

${\displaystyle \int 5dx}$ equals:

For $I_n={\displaystyle {\int }_0^1{x}^{n}dx}$, ${\lim }_{n\to \mathrm{\infty }}{I}_n$ equals:

Which statement is logically equivalent to "if $n^2$ is even, then $n$ is even"?

For $A=\left(\begin{array}{cc}1& 0\\ 0& 2\end{array}\right)$ and $B=\left(\begin{array}{cc}2& 4\\ 6& 8\end{array}\right)$, solve $XA=B$. Then $X$ equals:

The value of $\cos \text{\hspace{0.17em}⁣}(-{\displaystyle \frac{\pi }{3}})$ is:

If $\det (A)=3$ and $\det (B)=-2$, what is $\det (AB)$?

The set of units (multiplicatively invertible elements) of ${\mathbb{Z}}_8$ is:

The number of permutations of $(1,2,3,4)$ in which no element is in its original position is:

For the ellipse ${\displaystyle \frac{x^2}{25}}+{\displaystyle \frac{y^2}{9}}=1$, the eccentricity equals: