trig and inverse trig derivatives and integrals

Question 1

d/dx cot

Answer 1

-csc^2

Question 2

d/dx csc

Answer 2

-csccot

Question 3

d/dx sin

Answer 3

cos

Question 4

d/dx cos

Answer 4

-sin

Question 5

d/dx tan

Answer 5

sec^2

Question 6

d/dx sec

Answer 6

sectan

Question 7

d/dx arcsin

Answer 7

1 / sqrt(1 - x^2)

Question 8

integral of tan

Answer 8

-ln|cos| + c or ln|sec| +c

Question 9

integral of 1 / sqrt.(a^2 - x^2)

Answer 9

arcsin(x/a) + c

Question 10

integral of 1/(a^2 + u^2)

Answer 10

(1/a)arctan(u/a) + c

Question 11

shell method

Answer 11

rectangle is paralell; 2pi
vertical rectangle:
2pi*intphdx
horizontal:
2pi*intphdy

Question 12

shell method - what is p and h

Answer 12

p: distance from function to axis of revolution
h: height of rectangle (function +/- distance to axis)

Question 13

disk method

Answer 13

rectangle is perpendicular; pi*integral of r(X)^2

Question 14

washer method

Answer 14

rectangle is perpendicular; pi*integral of r(X)^2 - r(X)^2