Daily Math · 2026-06-08

Question 1

The area under the curve $y = x^2$ between $x = 0$ and $x = 3$ equals:

Accepted Answer

$\int_0^3 x^2 \, dx = \dfrac{27}{3} = 9$.

Answer

$3$

Answer

$6$

Answer

$9$

Answer

$27$

Question 2

$\displaystyle\int_0^{\pi/2} \sin^2 x \,dx$ equals:

Accepted Answer

$\int_0^{\pi/2} \sin^2 x\,dx = \int_0^{\pi/2} \dfrac{1-\cos 2x}{2}\,dx = \dfrac{1}{2}\left[x - 	frac{\sin 2x}{2}ight]_0^{\pi/2} = \dfrac{\pi}{4}$.

Answer

$	frac{\pi}{4}$

Answer

$	frac{\pi}{2}$

Answer

$1$

Answer

$	frac{1}{2}$

Question 3

The total number of asymptotes (vertical + horizontal + slant) of $f(x) = \dfrac{x^2 + 1}{x^2 - 1}$ is:

Accepted Answer

Vertical: $x = \pm 1$ (two). Horizontal: $\lim f(x) = 1$ (one). Total: $3$. (No slant — the rational function has equal-degree numerator and denominator.)

Answer

$1$

Answer

$2$

Answer

$3$

Answer

$4$

Problems & worked solutions

Problem 1 — Definite Integrals

Problem 2 — Calculus

Problem 3 — Asymptotes