MAT 21B Lecture Notes - Lecture 7: Quotient Rule, Power Rule, Product Rule

• School: UC-Davis
• Department: Mathematics
• Course: MAT 21B
• Professor: David Cherney

Document Summary

(cid:1856) constant c is not necessary since they cancel out one another. change the lower and upper limits of integration to express them in terms of u. Mat 21b - lecture 7 the u-substitution method and integration rules: example: evaluate the definite integral (cid:884)(cid:1857)2 (cid:2870)(cid:2868) Let i = (cid:884)(cid:1857)2 (cid:1856) and u = (cid:2870) (cid:3642)(cid:1856)=(cid:884)(cid:1856). Then i = (cid:1857)(cid:2870)(cid:2868) (cid:1856)= [(cid:1857)+](cid:2868)(cid:2870)= (cid:2870)(cid:2868) Another variation of solving this same problem is to. When evaluating definite integrals, adding the (cid:1856) : a common mistake in solving a problem such as this one is: (cid:884)(cid:1857)2 (cid:2870)(cid:2868) (cid:1857)(cid:2870)(cid:2868) (cid:1856)= [(cid:1857)](cid:2868)(cid:2870)= (cid:1857)(cid:2870) (cid:1857)(cid:2868)= (cid:1857)(cid:2870) (cid:883) which is incorrect: example 2: evaluate (cid:4666)(cid:884) 4(cid:4667)(cid:2871) (cid:1856) (cid:2869)(cid:2868) (cid:1856) and u = 2 4x (cid:3642)(cid:1856)= 4(cid:1856) (cid:3643)(cid:1856)= (cid:2869)(cid:2872)(cid:1856). 2 such that i = (cid:2869)(cid:2872) (cid:2871) (cid:1856). Let i = (cid:1858) ((cid:1859)(cid:4666)(cid:4667))(cid:1859) (cid:4666)(cid:4667) (cid:1856) (cid:3029)(cid:3028) (cid:1858) (cid:4666)(cid:4667) (cid:1856)