Hello, I am having an extremely diffucult time understanding trig subs in Calc2. Can someone please fully expalin to me why the limits of integration change from 3sqrt3/2 to pi/3?....and than change once again from 1 to 1/2. I know you can plug the number somewhere to see if they change, but I'm not sure where to do this...or even WHY to do this? I still don't understand why we change limits of integration in other calc problems like u-sub. Can you please explain it like you're explaining it to someone who has no math skills. I really appreiciate a clear explanation without too much math terminology.
God bless and thank you!
(3,3/2 o (4x2 +9) da BREMPLE Find SOLUTION First we note that (4x2 + 9) = (v4x 9 ) so trigonometric s is appropriate. Although v4x2 + 9 is not quite one of the expressions in t trigonometric substitutions, it becomes one of them if we make the prelim tion u 2x. When we combine this with the tangent substitution, we have which gives dr-2 sec 2 θ dθ and ric sub e tabl ary sub When x-0, tan θ = 0, so θ = 0: when x = 3 v/3/2, tan θ = v/3, so θ= Ï/3. o (4x2 + 9)3/2 6 Jo cos 0 16 10 Jo sec θ 16 cos20-sin θ d θ Now we substitute u = cos θ so that du--sin θ de when θ-0, 11-1; when θ-Ï/3, u = 2. Therefore 3v3/2 lu dx o (4x2 +9)3/2 lu =la[(1 + 2) _ (1 + 1)]= 32
