Chapter 5 Student.pdf - Chapter 5 Applications of...

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Chapter 5. Applications of Integration5.1 Area between Curves5.2 Volumes5.3Volumes by Cylindrical Shells5.5Average Value of a Function5.4Work1
5.1 Area Between CurvesRecall: Riemann Sums2
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Area Between Curves4
Example. Find the area of the region bounded above by ! = #$+ 1bounded below by ! = #, and on the sides by # = 0and # = 1., 5
$.6
Area Between Curves7
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Example. Find the area of the region enclosed by the line ! = # − 1and the parabola
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Integrating with Respect to ySometimes it’s difficult to find the top and bottom functions, so can look at the y-axis and use the right and left functions!!!10
Example. Find the area of the region bounded by ! = #$, ! = # + 6, and the x-axis.11
Summary for Finding Area1.Sketch the graphs and find the bounds.2.To find the area, use 12(topbottom)dxab(rightleft)dycd
5.2 Volumes13
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Example. Show that the volume of a sphere of radius !is " =$%&!

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