june 12 2019 mat136 week 3 justin ko 1 integration by substitution change of variables we can think of integration by substitution as the counterpart of the chain rule for ...
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...June mat week justin ko integration by substitution change of variables we can think as the counterpart chain rule for dierentiation suppose that g x is a dierentiable function and f continuous on range given following formulas indenite integral version z dx u du where denite bf b example problems strategy idea to make easier compute doing start guessing what appropriate variable should be usually you choose inside dierentiate both sides conclude if have use fact also bounds rewrite replacing all instances with new or computed then sure write your nal answer back in terms original problem find tan solution step will cos sin now evaluate under this ln c xe page xdx e remark instead changing rst nd fundamental theorem calculus tanh since remove absolute values wish giving ex cosh d form may remember it mirrors p udu...