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Learn to find area between curves by using horizontal strips instead of vertical ones. Simplify integration by avoiding two-part process. Discover the ease of utilizing horizontal strips that touch both curves, eliminating the need for multiple integrals. Solve for strip length using strip width dy. Example and step-by-step solution provided for better understanding. Apply the method to find region enclosed by curves. Embrace the convenience of dy integration for cohesive calculations. Determine bounds and solve for intersection to compute area accurately. Utilize a calculator for precision.
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8.2B – Area between to curves • Goal: find the area by using horizontal strips rather than vertical.
Example If we use the method we learned in 8.2A, we would have to integrate in two parts:
But there is an easier way! We can find the same area using a horizontal strip. Notice, now the horizontal strips will touch both curves no matter where we draw them, so we don’t need two integrals.
Since the width of the strip is dy, we find the length of the strip by solving for x in terms of y.
Solution Limits are y values. width of strip length of strip
Let’s do one together! • Find the area of the region enclosed by • Woa! We have Let’s solve it for y. • No graph all three curves.
Solution • Easier to use dy so you don’t have to split it up into 2 integrals. • So: Solve each equation for x. • (Already given)
Continued… • Bounds: We can see the lower bound is y=-1, and the upper bound we have to find the intersection. y=1.793003715 • Use calculator: Area is about 4.21 units squared.
