To find the area between curves, we will add tiny rectangles with width dx or dy and height found by the difference between curves.

General Notes

***Here we only care about the area between the curves themselves, not if there’s a gap in the axis or rotating anything, so it’s just top/right curve - bottom/eft

Integrating with respect to x:

$$ Area=∫(top-bottom)dx $$

Integrating with respect to y:

$Area=∫(right-left)dy$

Knowing when to use dx or dy:

• Use dx (integrating with respect to x) when equations are solved for y like $y=x^2$
• Use dy (integrating with respect to y) when equations are solved for x like $x=y^3$

Steps on solving these equations:

1. Identify top and bottom curve and their intersections (when functions equal each other)
2. Determine the interval of the area
3. Decide direction of stacking dx vertical or dy horizontal
4. Find dimensions by either top-bottom or right-left