# october11 - Areabetween2curves Sec\$on6.1(conclude VERTICAL...

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Area between 2 curves. Sec\$on 6.1 (conclude)

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upper func)on lower func)on VERTICAL INTEGRATION Given 2 func2ons of x: y=f(x) and y=g(x), defined over [a,b], find the area of the region enclosed between the 2 graphs. right‐most value of x le<‐most value of x A=?
Right func)on LeD func)on biggest value of y smallest value of y A=? HORIZONTAL INTEGRATION Given 2 func2ons of y: x=f(y) and x=g(y), defined over [c,d], find the area of the region enclosed between the 2 graphs.

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Find the area bounded by y=2x 2 +10 and y=4x+16 It is faster to compute the area by means of A. Horizontal Integration (in dy) B. Vertical Integration (in dx)
Find the area bounded by y=2x 2 +10 and y=4x+16 1) graph … to see which kind of integra)on is more convenient 2) find the extremes of integra2on a=‐1 b=3 Lower func)on Upper func)on a‐=‐1 b=3 Easy, by Vertical Integration

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Find the area bounded by y=2x 2 +10 and y=4x+16 Lower func)on Upper func)on a‐=‐1 b=3 ) )
Find the area bounded by y=2x 2 +10, y=4x+16, x=‐2 and x=5 The extremes of

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• Fall '09
• FAMIGLIETTI,C
• Calculus, Vertical market, Archimedes, Horizontal integration, B. Vertical integration

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