MAT136H1 Chapter Notes - Chapter 1d: Antiderivative

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: Al- Faisal, Faisal

Document Summary

The fundamental theorem of calculus (part ii, net change theorem) says that : If (cid:1858) is a continuous function on [(cid:1853),(cid:1854)], (cid:1856)=(cid:1858)(cid:4666)(cid:1854)(cid:4667) (cid:1858)(cid:4666)(cid:1853)(cid:4667). Then (cid:1858) (cid:4666)(cid:4667) (cid:3029)(cid:3028) (cid:1856)= 9 (cid:886: 9(cid:2872) (cid:1856)=(cid:4672)(cid:2870)(cid:2871)(cid:4673) 9(cid:2871) (cid:4672)(cid:2870)(cid:2871)(cid:4673) (cid:886)(cid:2871, 9(cid:2872) (cid:1856)= (cid:2869)(cid:2870) 9 (cid:2869)(cid:2870) (cid:2872, 9(cid:2872) (cid:1856)= (cid:2870) 9 (cid:2870) (cid:2872, 9(cid:2872) The (cid:884) parts of the: the construction theorem : if we take the derivative of the integral of (cid:1858), we get (cid:1858) back. Integration is actually an integral defining a function. (cid:1858)(cid:4666)(cid:1872)(cid:4667) (cid:3028: the net change theorem : if we take the integral of the derivative of (cid:1858), we get information about (cid:1858) back. We get information about how the (cid:1858) changes. Question : always, sometimes, or never ? part ii. If (cid:1858)(cid:4666)(cid:4667) is a continuous function on the interval [(cid:1853),(cid:1854)], then (cid:3029) (cid:1856)=(cid:887)+(cid:885) (cid:1858)(cid:4666)(cid:4667) (cid:1856) (cid:3028) (cid:887)+(cid:885)(cid:1858)(cid:4666)(cid:4667) (cid:3028) (cid:887) (cid:1853) (cid:1854: always, sometimes, never.