IB AA SL: Core and Optional Content Core: Vertical strips and integration with respect to $x$. Opt

Question

IB AA SL: Core and Optional Content

Core: Vertical strips and integration with respect to $x$.
Optional: Horizontal strips and integration with respect to $y$.

Vertical strips

$A=\int_a^b[\mathrm f(x)-\mathrm g(x)]\,\mathrm dx\quad(\mathrm f\ge \mathrm g,\ a<b)$

Horizontal strips

$A=\int_a^b[\mathrm f(y)-\mathrm g(y)]\,\mathrm dy\quad(\mathrm f\ge \mathrm g,\ a<b)$

Use upper minus lower for vertical strips, or right minus left for horizontal strips. Split wherever the boundary order changes.

Accepted Answer

With respect to $x$: $A=\int_a^b(\text{top}-\text{bottom})\,\mathrm dx$ With respect to $y$: $A=\int_c^d(\text{right}-\text{left})\,\mathrm dy$

Area Between Two Curves