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MAT 266 Lecture Notes - Lecture 7: Pythagorean Theorem

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limecrow851
20 Feb 2018
School
ASU
Department
Mathematics
Course
MAT 266
Professor
Faris Odish

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Document Summary

Group 4: used for integration of tan and cot to an even power** Distribute the (-) to each term (sec2(x) and the -1) = tan2(x)sec2(x) - sec2(cid:894)x(cid:895) + dx u = tan(x), du= sec2(x)dx. = u2du tan(x) + x + c. = 1/3 tan3(x) tan(x) + x + c. Sec(cid:894)x(cid:895)dx = ln |sec(cid:894)x(cid:895) + tan(cid:894)x(cid:895)| + c. Csc(cid:894)x(cid:895)dx = ln |csc(cid:894)x(cid:895) cot(x)| + c. Example: prove that tan(cid:894)x(cid:895)dx = ln |sec(cid:894)x(cid:895)| + c. Substitution x=asin , - x=atan , - (cid:888) (cid:888)< < x=asec , 0 < (cid:888) (cid:888) (cid:888) < (cid:889) (cid:888) Call x = 2sin , - (cid:888) . Call dx = 2cos equation 2 (cid:888) (cid:890) (cid:888) (cid:890) (cid:890) . Using both equation 1 and 2 (cid:887) (cid:890) (cid:887) (cid:890) (cid:888) . equation 1 (cid:888) (cid:890) (cid:888) (cid:888) . the 2cos are canceling with each other (cid:887) (cid:887) (cid:890) cot( (cid:4667) + c (***) find the cot ( (cid:4667) in the (***) equation above.

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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.

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