Math 124 Name _______________#39 Second Fundamental Theorem of Calculus 6.4Let dxxfxF )()( where ).()( xfxF 1. Let .)(3xxf Then CxdxxxF4341)(.What if )(xf were some strange function that we couldn’t antidifferentiate? We could still write dxxfxF )()(2. Let xdtty23 where .)(3ttf (a) Is this a function?(b) What is the independent variable? Explain.(c) Let xdttxG33)(. Find G(x). Is G(x) in the same family as F(x)?(d) Find )(xF and ).(xG(e)CONCLUSION:xadttfAF )()( then F ‘(x) =(f)CONCLUSION:aadttAF3)((g)CONCLUSION:If )()()(xgadttfxF then F ‘(x) = 3.xtdtexE02)( is an antiderivative of 2xe.(a) Is E(x) increasing or decreasing and why?Math 124 Name _______________(b) Is E(x) concave up or concave down and why?(c) When are the values of E(x) positive and when are they negative and why?(d) Sketch a graph of E(x).4. Given the graph of f (x) below, sketch a graph of xdttfxF2)()(In the grid below, change the f(x) to
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