MATH 140 Lecture Notes - Lecture 24: Ibm Aix
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Solution if f is a function defineacn netareaunderthegraph from0 tox oo. aforaeriv. ph investigate acnoffctdt. A x offe at then aix f x t i s a lying kfh. If f is a continuousfunction and a x. Chdt then a is an antideriv of f a f ftp. fffttdt fx ex find thederivofthefollowing ex dt. A x coshy f s ex a11 1tfedt. 2 13 onaine derivot x2 2 ex aca. Iinchdt ex a x tf3dt ffedt offedt fedtt. A x sin sink cosh coax ex acn stan at. Ahi"s. fmtanctldttothanchdt ofianmnuiatitieanctidt tan sink cos tan cos x sincx. Awi aniantiderivof t offhdt off hdt offhdtoff t dt f"t"dt fat f o where f is anyantideriv of t f t tf 7. Ftc pt2 offxdx f b f a netarea. F isany deriv ex ol dx f i flo. Exofrxax f i flo where f isany antideriv oftx x 2 f x an ex 1 ax p ftp. ooob f isantiderivofx 2 fchit.
