Department

MathematicsCourse Code

MATH 2BProfessor

AllStudy Guide

MidtermThis

**preview**shows half of the first page. to view the full**3 pages of the document.**●What is the chain rule?

○Take the derivative of (x) sin(x)f= 2

○(x) cos(x) xf′= 2*2

●Undoing the chain rule

○Is harder to recognize when to undo the chain rule when finding the integral

●Instead, you can rewrite certain parts

○ =os(x)2xdx

∫c2os(u)du

∫c

○How?

■Set xu = 2

■Then take derivative of u

■x

dx

du = 2

■Then isolate du

■u 2xdxd =

■And substitute

○os(u)du

∫c

■Finish taking integral

■in(u) Cs +

■Replace u’s

■in(x) Cs 2+

Examples

●an (x)sec (x)dx

∫t7 2

○ tanxu =

○u sec dxd = 2

○du

∫u7

○u) C(8

18+

○(tanx) C

8

18+

●dx

∫1+x2

tan x

−1

Substitution

Section 5.5

Review

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