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**Unformatted text preview: **inite integral using FTC and properties of the denite integral. Shade the regions whose areas contribute to this denite integral. f ( x ) = 2 sin( x ) x < x x Z 1-1 f ( x ) d x = Is your answer positive or negative? What has more area: one hump of the function sin( x ), or the area under the square root function from 0 to 1 ? How much bigger is it? Just looking at your picture and thinking in terms of areas, is the function R x-1 f ( t ) d t increasing or decreasing at x =-1 2 ? at x = 0? at x = 1 2 ? Is it changing more rapidly at x = 1 2 or at x = 1?...

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