Calculus 2 Chapters 6-8 Flashcards
d/dx(sinx) =
cos x
d/dx (cos x)
- sin x
d/dx (tan x)
sec^2 x)
d/dx (sec x)
sec x tan x
d/dx (cot x)
- csc^2 x
d/dx (csc x)
- csc x cot x
d/dx a^x =
a^x ln a
d/dx (loga x) =
1/(x ln a)
sin^2 x + cos^2 x =
1
sin (A + B) =
sinAcosB + cosAsinB
cos (A + B) =
cosAcosB - sinAsinB
sin 2x =
2 sin x cos x
cos 2x =
cos^2 x - sin^2 x
cos^2 x =
(1 + cos 2x) /2
sin^2 x =
(1 - cos 2x)/2
integral of cos^2 x =
x/2 + sin2x/4 + c
integral of sin^2 x =
x/2 - sin 2x/4 + c
the disk method =
v = integral from a to b of pi(R(x))^2 dx
the washer method =
v = integral from a to b of pi[R(x)^2 - r(x)^2] dx
shell method =
v = integral of 2pi (shell height) (shell radius)
arc lengthe =
L = integral from a to b of square root 1 + [dy/dx]^2 dx
are of the surface generate by revolving graph around the x-axis =
S = integral from a to b of 2piy square root 1+(dy/dx)^2 dx
are of the surface generate by revolving graph around the y-axis =
S = integral from a to b of 2pix square root 1+(dx/dy)^2 dx
center of mass =
integral from a to b of (leverarm) (mass)/ integral of total mass
sinh x =
e^x - e^-x /2
cosh x =
e^x + e^-x / 2
integration by parts =
ulta violet voodoo
uv - integral of vdu du
sec^2 x =
1 + tan^2 x
