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MAT135H1 Study Guide - Antiderivative


Department
Mathematics
Course Code
MAT135H1
Professor
all

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Antiderivative*
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Knowledge*Summary:*
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The$antiderivative$is$the$operation$that$goes$backward$from$the$derivative$of$a$function$to$the$
function$itself.$Since$the$derivative$does$not$determine$the$function$completely$(you$can$add$any$
constant$to$your$function$and$the$derivative$will$be$the$same),$you$have$to$add$additional$
information$to$go$back$to$an$explicit$function$as$antiderivative.$$The$more$common$name$for$the$
antiderivative$is$the$indefinite$integral.$This$is$the$identical$notion,$merely$a$different$name$for$it.$
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The$definition$is:$
If$F$is$an$antiderivative$of$f$on$an$interval$I,$then$the$most$general$antiderivative$of$f$on$I$is$F(x)$+$C,$
where$C$is$an$arbitrary$constant.$
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Table$of$integration$formulas$that$are$useful:
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