MATH 2B Lecture Notes - Lecture 6: Dont

16 views5 pages

ultramarineporcupine570

27 Oct 2017

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

ferrari12 and 38332 others unlocked

$MATH 2B Full Course Notes$

MATH 2B Full Course Notes

Verified Note

74 documents

Document Summary

We know how to use the chain rule when taking the derivative. But do we know how to take the anti-derivative of a complex function? (cid:1858)(cid:4666)(cid:1876)(cid:4667)=sin(cid:1876)(cid:2870) (cid:1858) (cid:4666)(cid:1876)(cid:4667)=cos(cid:1876)(cid:2870)(cid:884)(cid:1876) =sin(cid:1876)(cid:2870)+(cid:1855: substitute the u in for (cid:1876)(cid:2870). We chose (cid:1876)(cid:2870) instead of 2x because (cid:1876)(cid:2870) is what is being chain (cid:1873)=(cid:1876)(cid:2870) (cid:1856)(cid:1873)=(cid:884)(cid:1876)(cid:1856)(cid:1876) Ge(cid:374)erally, this (cid:373)ethod is (cid:272)alled (cid:862)u-su(cid:271)stitutio(cid:374). (cid:863) ruled. Example #6: (cid:1873)=(cid:1872)(cid:1866) (cid:2869)(cid:4666)(cid:1876)(cid:4667) (cid:1856)(cid:1873)= (cid:2869)(cid:2869)+(cid:3051)(cid:3118) (cid:1856)(cid:1876) (cid:1873)=sin(cid:4666)(cid:4667) (cid:1856)(cid:1873)=cos(cid:4666)(cid:4667)(cid:1856) (cid:1873)=cos(cid:4666)(cid:4667) (cid:1856)(cid:1873)= sin(cid:4666)(cid:4667)(cid:1856) (cid:1873)=(cid:887)+(cid:885)(cid:1876)(cid:2870) (cid:1856)(cid:1873)=(cid:888)(cid:1876) (cid:1856)(cid:1876) (cid:2869)(cid:2874)(cid:1856)(cid:1873)=(cid:1876) (cid:1856)(cid:1876) (cid:1873)= (cid:1876) (cid:884)(cid:1856)(cid:1873)=(cid:1876) (cid:3117)(cid:3118) (cid:1856)(cid:1876) (cid:1873)=(cid:1876)(cid:2870) (cid:3031)(cid:2870)=(cid:1876)(cid:1856)(cid:1876) Or, if you really don"t want to do a double u-sub, do a good 1st substitution. (cid:1873)=cos (cid:4666)(cid:1876)(cid:2870)(cid:4667) (cid:1856)(cid:1873)= sin(cid:4666)(cid:1876)(cid:2870)(cid:4667) (cid:884)(cid:1876)(cid:1856)(cid:1876) Now that we know how to u-su(cid:271) usi(cid:374)g i(cid:374)defi(cid:374)ite i(cid:374)tegrals, let"s try su(cid:271)stitutio(cid:374) with defi(cid:374)ite integrals. What we did here was leave x=1 and 1=e as the interval for x because if we put the interval as. [1,e] for u, that would change our integral completely.

Related Questions

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!