lecture33 - -1 1 1 Example 3 Find the area bounded by f x =...

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Math 006 (Lecture 33) Area between two curves Consider the area bounded by y = f ( x ) and y = g ( x ), where f ( x ) g ( x ) 0, for a x b Area between f ( x ) and g ( x ) = (area under f ( x )) - (area under g ( x )) = Z b a f ( x ) dx - Z b a g ( x ) dx = Z b a [ f ( x ) - g ( x )] dx Example 1. Find the area bounded by f ( x ) = 6 x - x 2 and y = 0 for 1 x 4. Example 2. Find the area between the graph of f ( x ) = x 2 - 2 x and the axis over the intervals: (a) [1 , 2] (b) [
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Unformatted text preview: -1 , 1] 1 Example 3. Find the area bounded by f ( x ) = 5-x 2 and g ( x ) = 2-2 x Example 4. Find the area bounded by f ( x ) = x 2-x and g ( x ) = 2 x for-2 ≤ x ≤ 3. Example 5. Find the area bounded by f ( x ) = 2 x 2 and g ( x ) = 4-2 x for-2 ≤ x ≤ 2. 2...
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lecture33 - -1 1 1 Example 3 Find the area bounded by f x =...

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