["ª f(x) dx = af (a) - [² xf'(x) dxFirst use Integration by Parts. Then assume f(x) is increasing or de-= f(x) to prove thatracreasing. Use the substitution u =S²² xf'(x) dx isequal to the area of the shaded region in Figure 1 and derive Eq. (8) anovollsecond time.yf(a) +f(0)vollot sniglasnayaLoirib one vad 0y = f(x)bho as mimolgex- XInonoqxo aFIGURE 1

[² f(x) dx = af (a) — ["² xf'(x) dx First use Integration by Parts. Then assume f(x) is increasing or de- ra creasing. Use the substitution u = f(x) to prove that f" xf'(x) dx is equal to the area of the shaded region in Figure 1 and derive Eq. (8) a second time. 101081 15V f(a) f(0) birib ons vad 0 y = f(x) - vainonoqxo a FIGURE 1 8 X oivi

[² f(x) dx = af (a) — ["² xf'(x) dx First use Integration by Parts. Then assume f(x) is increasing or de- ra creasing. Use the substitution u = f(x) to prove that f" xf'(x) dx is equal to the area of the shaded region in Figure 1 and derive Eq. (8) a second time. 101081 15V f(a) f(0) birib ons vad 0 y = f(x) - vainonoqxo a FIGURE 1 8 X oivi

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 20CR

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