MATH 1041 Chapter Notes - Chapter 5: Integral Symbol, Differentiable Function, Antiderivative

• School: Temple University
• Department: Mathematics
• Course: MATH 1041
• Professor: farhanabedin

Document Summary

5. 1 areas and distances the sum of the areas of approximately rectangles the area of the region (cid:1845) that lies under the graph of the continuous function (cid:1858) is the limit of. Example let be the area of the region that lies under the graph of (cid:1858)(cid:4666)(cid:4667)=(cid:1857) between = (cid:882) and =(cid:884). Using right endpoints, find an expression for as a limit. Since (cid:1853)=(cid:882) and (cid:1854)=(cid:882), the width of a subinterval is. The sum of the areas of the approximating rectangles is (cid:1844)=(cid:1858)(cid:4666)(cid:2869)(cid:4667) +(cid:1858)(cid:4666)(cid:2870)(cid:4667) + +(cid:1858)(cid:4666)(cid:4667) . The symbol was introduced by leibniz and is called an integral sign. It is an elongated (cid:1845) and was chosen because an integral is a limit of sums. The procedure of calculating an integral is called integration. (cid:3029)(cid:3028) is called the defined by. The fundamental theorem of calculus, part 1 if (cid:1858) is continuous on [(cid:1853),(cid:1854)], then the function (cid:1859) (cid:1856)(cid:1872) (cid:1853) (cid:1854)