When calculating the area between two curves, $f(x)$ and $g(x)$, if they intersect multiple times, what is the correct approach to setting up the integral(s)?
Question 2
Given the curves $y = x^2 - 4$ and $y = 0$, what are the limits of integration for finding the area of the region bounded by these curves?
Question 3
If the area between two curves $y = f(x)$ and $y = g(x)$ is calculated with respect to $y$ (i.e., using $x = f(y)$ and $x = g(y)$), what is the general formula for the area over the interval $[c, d]$?
Question 4
Calculate the area between the curves $y = x^2$ and $y = x + 2$.
Question 5
If the curves $y = f(x)$ and $y = g(x)$ are such that $f(x) \ge g(x)$ over the interval $[a, b]$, and $g(x)$ is below the x-axis, how does this affect the calculation of the area between them?
Area Between Curves Quiz — AS-Level Mathematics | A-Warded
