Definitions [1]
Definition: Symmetrical Area
If a curve is symmetrical about a line, axis, or origin, then the total area can be obtained by finding the area of one symmetrical part and multiplying it by the number of such parts.
Key Points
Key Points: Area Under Simple Curves
- \[\mathrm{A}=\int_{x=a}^{x=b}y\mathrm{d}x=\int_{a}^{b}\mathrm{f}(x)\mathrm{d}x\]
- If below x-axis → use |f(x)|
- Area w.r.t. Y-axis →\[\mathrm{A}=\int_{y=c}^{y=d}x\mathrm{d}y=\int_{c}^{d}\mathrm{f}(y)\mathrm{d}y\]
- If the curve crosses the axis → split the interval
Key Points: Area Bounded by Two Curves
- A = ∫ (upper − lower) dx
- Find intersection points → solve f(x) = g(x)
- If the graph crosses → split into parts
- Final area = sum of all parts
