Chapter 23 - Integration 2 (Pure)

Question 1

∫ (ax+b) ⁿ =?

Answer 1

∫ (ax+b) ⁿ = 1/ a (n+1) (ax+ b) ⁿ + C

Question 2

∫ 1/x = ?

Answer 2

∫ 1/x = ln [x] + c

Question 3

∫ 1/ ax + b = ?

Answer 3

∫ 1/ ax + b = 1 / a ln [ ax+ b ] + C

Question 4

∫ e^ax dx = ?

Answer 4

∫ e^x dx = 1/a e^x + c

Question 5

∫ e^ (ax + b ) = ?

Answer 5

∫ e^ (ax + b ) = 1/a e^(ax + b ) + C

Question 6

∫ sin ax dx = ?

Answer 6

∫ sinx dx = - 1/ a cosx + c

Question 7

∫ cos ax dx = ?

Answer 7

∫ cosx dx = 1/a sin x + c

Question 8

∫ sec² x = ?

Answer 8

∫ sec² x = 1/a tan ax + c

Question 9

∫ f’(x) / f(x) = ?

Answer 9

∫ f’(x) / f(x) dx = ln [f(x)] + c

Question 10

∫ du/dx f’(u) dx = ?

Answer 10

∫ du/dx f’(u) dx = f (u) + C

Question 11

the double angle formula, for sin(2A) = ?

Answer 11

sin(2A) = 2 sin A cos A

Question 12

the double angle formula, for cos(2A) = ?

Answer 12

cos(2A) = cos²A - sin²A

Question 13

the double angle formula for tan 2A = ?

Answer 13

tan 2A = (2 tan A)/ (1- tan²A)

Question 14

what’s ‘sexy tans’ ?

Answer 14

sec²x = 1 + tan²x

Question 15

what’s ‘cosey cots’ ?

Answer 15

cosec² x = 1 + cot² x

Question 16

what’s integration by parts? found on the data sheet…

Answer 16

∫ u dv/dx = uv -∫ v du/dx dx

L logarithms
Algebra
T trigonometry
E everything else

the order to choose u :)

Question 17

how to do integration by substitution?

Answer 17

step one - set u as inner of equation
step two - take integral of u
step three- take out dx and substitute in

(6x+ 1)^1/2 dx

u= 6x+1
du/dx = 6

u^0.5 X 1/6

1/9 (6X + 1) ^3/2 + C