M408C- Brian's Draf Cheat Sheer

M408C- Brian's Draf Cheat Sheer - Area BTW Curves-Find...

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Area BTW Curves -Find Intercepts -Integrate Between Intercepts a1a2fx- gxdx-a2a3fx- gx + Want Positive Area Hyperbolic Trig lnx=y = ey=x ln1=0 lnx=1 lne=1 lnab=ln a+lnb lnab=lnx-lny lnan=nlna 1xdx= lnx+ c lnxdx=xlnx- x+c dydx1x=-1x2 dxx±a=lnx±a+ c y xlnx=1x ∂ ∂ y x ex =ex ∂ ∂ y x eu =eududx ∂ ∂ coshx=ex+e-x2 sinhx=ex-e-x2 dydxsinhx=coshx dydxcoshx=sinhx sinhx=coshx + c coshx=sinhx + c Critical Points -CP = f-1x= 0 or undefined First Derivative Test - Separate interval according to intercepts - Find the sign of f-1x on each interval - fx: + - then local min - fx: - + then local max - Integration by Parts - udv=uv- udv - Trig Substitution - 1x2-a2dx= 1atan-1xa + C - 1a2-x2dx= sin-1xa + C - 1xx2-a2dx= 1asec-1xa+ C - dydxtan-1x= 11+x2 - dydxsin-1x= 11-x2 - dydxsec-1x= 1xx2-1 - x2-a2=x=asecx - x2+a2=x=atanx - a2-x2=x=asinx - Product of Trig Functions - cosmx sinnx dx - M odd o Save 1 cosx and write the rest as sin x; U = sin x - N Odd o Save 1 sin x and write the rest as cos x; U = cos x - Otherwise: Everything as sin x; Use recursion
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