MATH 101 Lecture 1: Areas and Distances: Introduction to integration concepts
Document Summary
Math 101: 5. 1: areas and distances, lecture 1 5th january, 2015. Last term in math 100: all about tangent lines to curves derivatives (useful: rate of change, optimization) This term 101: all about area integral (useful: compute work for forces, solve differential equations) Areas are easy to calculate and compute for shapes with straight sides. However, it is a slightly different process to calculate areas under graphs. 3 ways to find definite integrals: find limits of riemann sums, areas (don"t forget negative when f(x) is less than equal to 0, find derivative using the fundamental theorem of calculus. X2dx: approximate using midpoints on 3 subintervals a. =251/108 (7/6 2 (1/3))+ (9 /6 2 (1 /3)) (11/6 2 (1/3)) Area of the figure = 0. 25(9 .
