Calculus 2 Chapters 6-8

Question 1

d/dx(sinx) =

Answer 1

cos x

Question 2

d/dx (cos x)

Answer 2

• sin x

Question 3

d/dx (tan x)

Answer 3

sec^2 x)

Question 4

d/dx (sec x)

Answer 4

sec x tan x

Question 5

d/dx (cot x)

Answer 5

• csc^2 x

Question 6

d/dx (csc x)

Answer 6

• csc x cot x

Question 7

d/dx a^x =

Answer 7

a^x ln a

Question 8

d/dx (loga x) =

Answer 8

1/(x ln a)

Question 9

sin^2 x + cos^2 x =

Answer 9

1

Question 10

sin (A + B) =

Answer 10

sinAcosB + cosAsinB

Question 11

cos (A + B) =

Answer 11

cosAcosB - sinAsinB

Question 12

sin 2x =

Answer 12

2 sin x cos x

Question 13

cos 2x =

Answer 13

cos^2 x - sin^2 x

Question 14

cos^2 x =

Answer 14

(1 + cos 2x) /2

Question 15

sin^2 x =

Answer 15

(1 - cos 2x)/2

Question 16

integral of cos^2 x =

Answer 16

x/2 + sin2x/4 + c

Question 17

integral of sin^2 x =

Answer 17

x/2 - sin 2x/4 + c

Question 18

the disk method =

Answer 18

v = integral from a to b of pi(R(x))^2 dx

Question 19

the washer method =

Answer 19

v = integral from a to b of pi[R(x)^2 - r(x)^2] dx

Question 20

shell method =

Answer 20

v = integral of 2pi (shell height) (shell radius)

Question 21

arc lengthe =

Answer 21

L = integral from a to b of square root 1 + [dy/dx]^2 dx

Question 22

are of the surface generate by revolving graph around the x-axis =

Answer 22

S = integral from a to b of 2piy square root 1+(dy/dx)^2 dx

Question 23

are of the surface generate by revolving graph around the y-axis =

Answer 23

S = integral from a to b of 2pix square root 1+(dx/dy)^2 dx

Question 24

center of mass =

Answer 24

integral from a to b of (leverarm) (mass)/ integral of total mass

Question 25

sinh x =

Answer 25

e^x - e^-x /2

Question 26

cosh x =

Answer 26

e^x + e^-x / 2

Question 27

integration by parts =

Answer 27

ulta violet voodoo

uv - integral of vdu du

Question 28

sec^2 x =

Answer 28

1 + tan^2 x