[SOLVED] Integration with Trigonometric Substitution 1. The problem statement, all variables and given/known data Given integral (I): I[(x)sqrt(9-x^2)dx] by words: Integral of "X" times square root of "9-X(squared) Use proper trigonometric substitution to solve this problem. 2. Relevant equations 3. The attempt at a solution
You don't even need Trig substitution. [tex]\int x\sqrt{9-x^2}dx[/tex] [tex]u=9-x^2[/tex] [tex]du=-2xdx \rightarrow xdx=-\frac 1 2 du[/tex]
Well you posted the solution to it? I don't know what else to tell you. Just analyze what they did. Work it yourself a couple times if you have to.
You forgot a term when you first did the substitution. x = 3sin(u) dx = 3cos(u)du (9 - x^2)^(1/2) = 3cos(u) So the integral becomes 27sin(u)cos^2(u)du