2007-11-07 A Geometric Interpretation

2007-11-07 A Geometric Interpretation - .,.~. . the...

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I l A Geometric Interpretation If the values of I are positive, tP.eequation d J X dx I(t) dt = I(x) a has a nice geometric interpretation: The integral of/from a.to x is the area A(x) of the region between the graph of I and the x-axis from a to x . Imagine the area swept out by a wiper blade clearing the .raindrops from the win"shield on a bus. .As the blade moves past x, the rate at which the cleared area is being swept out is precisely
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Unformatted text preview: .,.~. . the heig11fof the vertical blade I(x), y y = /(t), heightof verticalblade--------t ..f A(x) = cleared area a x . The rate at which the wiper blade on a bus clears the windshield of rain as the blade moves past x is the height of the blade. In symbols, dA/dx =f(x)....
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