C3

Question 1

product rule

Answer 1

dy/dx = u dv/dx + v du/dx

Question 2

quotient rule

Answer 2

dy/dx = v du/dx - u dv/dx / v^2

Question 3

integration by parts

Answer 3

f(u dv/dx)dx = uv - f(v du/dx)dx

Question 4

differentiate sinx

Answer 4

cosx

Question 5

differentiate cosx

Answer 5

-sinx

Question 6

integrate sinx

Answer 6

-cosx

Question 7

integrate cosx

Answer 7

sinx

Question 8

integrate tanx

Answer 8

lnsecx

Question 9

differentiate tanx

Answer 9

sec^2x

Question 10

integrate 1/ax+b

Answer 10

1/a ln|ax+b|

Question 11

differentiate lnx

Answer 11

1/x

Question 12

integrate f’(x)/f(x)

Answer 12

ln|f(x)|

Question 13

differentiate f(ax+b)

Answer 13

af’(ax+b)

Question 14

identity involving sec and tan

Answer 14

sec^2x = 1 + tan^2x

Question 15

identity involving cosec and cot

Answer 15

cosec^2 = 1 + cot^2x

Question 16

integrate e^ax

Answer 16

1/a e^x

Question 17

solids of revolution about the y axis

Answer 17

π f x^2 dy

Question 18

mid ordinate rule

Answer 18

area = h x sum of mid ordinates

Question 19

simpson’s rule

Answer 19

area = 1/3 h (sum of end ordinates +4(sum of odd ordinates) + 2(sum of remaining even ordinates))