lecture 33 the denite integral and its applications cont d using denite integrals instead of indenite integrals antiderivatives in solving problems there is no relevant section in the textbook by ...
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...Lecture the denite integral and its applications cont d using integrals instead of indenite antiderivatives in solving problems there is no relevant section textbook by stewart for material presented today s previous we discussed an important application fundamental theorem calculus ii namely that z bf x dx f b a this true any dierentiable function since denition antiderivative quantity on left hand side equation represents integration rate change from to right net discusses number property indeed examined classical mechanics suppose v t velocity particle travelling straight line represented axis relation position course dt which simply consequence ftc have bv bx other words over time interval displacement now consider slightly dierent form above ll integrate starting say future but keep upper limit as variable with regard replace means something else result ds may be rewritten follows ztv can veried dierentiation derivative lhs constant rhs i use idea repeatedly areturn near earth fal...