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Explain area between curves (y).
Area is found by integrating the absolute difference between two functions with respect to $y$, from $c$ to $d$ on the y-axis.
Why use absolute value in the area formula?
To ensure that the area is always positive, regardless of which function is greater.
How do horizontal slices help?
They allow us to integrate with respect to $y$, summing up the areas of infinitesimally thin rectangles to find the total area.
Explain the importance of limits of integration.
The limits of integration define the interval over which the area between the curves is calculated.
How does a calculator help?
A calculator can evaluate definite integrals, find intersection points, and graph functions to visualize the area.
Formula for area between curves (y)?
$A = \int_{c}^{d} |f(y) - g(y)| , dy$
How to find intersection points?
Set the two functions equal to each other and solve for $y$.
Graph of $f(y) > g(y)$?
The area between the curves is found by integrating $f(y) - g(y)$ over the interval where $f(y)$ is above $g(y)$.
How to use the graph to find intersection points?
Intersection points are where the curves intersect on the graph; these points determine the limits of integration.