MATH 1151 Lecture 44: Substitution (continued)

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1151
• Professor: Dong Chen

Document Summary

We should try to eliminate x in the expression. You need to be flexible to find the right u. Take u to be the inner function of f(x) Take u to be the denominator of a fraction. Compute du after choosing one to be the u. Example: (chen 4) u = sin x du = cos x dx. By replacing complicated parts in the function with u and du, we can rewrite the function as integral (sec u)^2 du. Next, find the antiderivative of (sec u)^2 du tan u + c = tan(sin x) + c. Make u = ln x du = 1/x dx. Change the end points from [1, e^(pi/4)] to [0, pi/4] Example: (chen 5) u = 1 - x^2 du = -2xdx. Then du = -1/(2 sqrt x) dx = -2sqrt x du. X=0, u=4 (bound changed) x=16, u=0 (chen 6) Example: (chen 8) tan x = sin x / cos x.