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.