AppIntegday2notes - Region D Area = f x dx a b Area = f...

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Calculus Applications of Integration Page 5 Applications of Integration Day 2 More on Area Between Curves and using the Calculator Example 1 Example 2 Find the area between y = sec 2 x and y = sin x Find the area enclosed by from x = 0 to x = π 4 y = 2 x 2 and y = − x Example 3 Find the area enclosed by y = 2cos x and y = x 2 1
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Calculus Applications of Integration Page 6 Example 4 Find the area bounded by y = x and the x-axis and the line y = x 2 There exists another way to determine the area above – take a horizontal slice.
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Calculus Applications of Integration Page 7 Example 5 Find the area enclosed by y = x 3 and x = y 2 2 Example 6 Find the area bounded by x = − y 1 ( ) y 3 ( ) and the y-axis Assignment V-2 Pages 380 – 382 #1-10 all, 11-15 odd, 18, 31, 33 (use calculator)
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Calculus Applications of Integration Page 8 Summary Concept I Area Region A Region B Region C
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Unformatted text preview: Region D Area = f x ( ) dx a b ∫ Area = f y ( ) dy c d ∫ Area = f x ( )− g x ( ) ( ) dx a b ∫ Area = f y ( ) − g y ( ) ( ) dy c d ∫ General Comments • Notice that a and b are on the x-axis c and d are on the y-axis • When using formulas involving f x ( ) you must solve for y for example: y = x 2 • When using formulas involving f y ( ) you must solve for x for example: y = x 2 → x = y • Look at the region and decide which way to slice vertical slices → dx → to x − axis horizontal slices → dy → to y − axis • Remember if using horizontal slices, write relations in the form " x =" • If finding total area, sometimes it is necessary to break up your integrals, for example Area = f x ( ) dx − a b ∫ f x ( ) dx b c ∫...
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AppIntegday2notes - Region D Area = f x dx a b Area = f...

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