Friday, november 20 lecture 30 : integration by substitution (refers to section. Students who have mastered the content of this lecture know: about differentials, integration by change of variable (equivalently, by substitution). Students who have practiced the techniques presented in this lecture will be able to: compute integrals by substitution correctly. Summary of what have learned about the notion of integration. Our study of integration began with attempts at finding the area of the region bounded by the curve of f(x) and the x-axis over an interval [ a, b]. To do this we introduced the notion of a riemann sum. But computing areas in this way is inefficient. The fundamental theorem of calculus presented an alternate way to compute such numbers. This important theorem is presented into two parts. That is, if f(x) is continuous on [a, b] and f(x) is an anti- derivative of f(x) then.
