[MATH 182A] - Midterm Exam Guide - Comprehensive Notes for the exam (110 pages long!)
Document Summary
Substitute unsolvable terms with u to reduce the equation to something easier to integrate. Let : u = 1 + cos(t) du = sin(t)dt dt = du sin(t) Substitute your new terms back into the original equation. The goal is to get a friendlier integral in terms of another variable. If the new integral has both x and u in it, then it may be advisable to try a di erent method of integration or substituting a di erent term. One we simplify the integral after substituting everything, it becomes much easier to integrate. Let : u = tan(x) du = sec2(x)dx u2. Finding the area between curves is very similar to nding the area underneath a curve. The area between f and g is simply the di erence between the area under f and the area under g. Find the area between the curves: y = 5x x2 y = x.
