Area of Bounded Regions

if f(x) is a continuous function defined on [a,b]. then, the area bounded by the curve y = f(x), the x-axis and the ordinates x = a and x = b is given by

∫f(x)dx(between limits a to b) or ∫y dx (between limits a to b).


Steps to find the area of bounded regions

1. visualize a rough sketch.

2. Slice the area into horizontal or vertical strips appropriately.

3. Create a formula for area treating the strip as a rectangle.

If the strip is parallel to y-axis, the width of the rectangle will be Δx.

If the strip is parallel to x-axis, the width of the rectangle will be Δy.

4. Find the limits of x (for vertical strips) and limits of y for horizontal strips.

5. Do the integration ∫ydx or ∫xdy
y = f(x) is the given function or x = f(y) is the given function.