MAT 1300 Lecture Notes - Lecture 12: Integral, Riemann Sum

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

Mat 1300 lecture 12 - the definite integral. A car travels at a constant speed of 40 km/hr for 2 hours how far has it gone. Answer : 40 km/hr *2 hr = 80 km. This is the same as the area of a rectangle. A car travels so that its speed increases steadily from 0 to 40 km/hr for 2 hours how far has it gone. It"s given by the area of a triangle. In general if f represents the rate of change" then the area of f underneath f represents the total change". Goal of integral calculus : compute this area. The definite integral of a continuous positive function f (positive means f(x) >= 0 for all x) over an interval [a,b] is the area between f , the x-axis , the line x=a amd the line x=b.