Woods, Frederick S. (Frederick Shenstone), 1864-, Bailey, Frederick H. (Frederick Harold), 1865- · Boston, New York [etc.] Ginn and Company · leaf 282
r f(x) dx = area ADPCB, Let m = AX and M=AHbe respectively the smallestand the largest value assumedby f(x) in the interval AB.Construct the rectangle A BKHwith the base AB and the alti-tude AM— M. Its area is AB • AH=(b - a)M. Construct alsothe rectangle ABLNwith the base AB and the altitude AN—… … 260 APPLICATIONS OF INTEGRATION Now it is evident that the area A BCD is greater than thearea ABLN and less than the area ABKH. That is, (b - a) m < f f(x) dx < (b - a) M*Consequently I f(x) dx = (b — a) /x, U a where fx, is some quantity greater than m and less than M, andis represented on…
Geometry, Analytic · Calculus
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