Integration P1 Flashcards
what is the integration of sinx
-cosx + c
what is the integration of cosx
sinx + c
what is the integration of 1/x
ln|x| + c
what is the integration of 1 / (ax + b)
1/a ln(ax + b) + c where (ax + b) is +ve
what is the integration of sin(ax + b)
-1/a cos(ax + b) + c
what is the integration of cos(ax + b)
1/a sin(ax + b) + c
what is the inverse of sin x
1 / cosec x
what is the inverse of cos x
1 / sec x
what is the inverse of tan x
1 / cot x
what does sin^2x + cos^2x =
1
what does sec^2x =
tan^2x + 1
what does 1 + cot^2x =
cosec^2x
what are the three C’s on the right side of the magic hexagon from top to bottom
- cos
- cot
- cosec
what are the three remaining functions on the left side of the hexagon, from top to bottom
- sin
- tan
- sec
what is the rule for working out the quotient identities
- going either clockwise or anti clockwise
- the identity you start off with = the next identity next to it divided by the identity next to that one
using the quotient rule, what are the two identities for cot
- cot = cos / sin
- cot = cosec / sec
what is the first rule for working out the product identities
- a function between any two functions
- is equal to those two functions multiplied together
using that first rule what is the product of tan and cos
tan cos = sin
what is in the middle of the hexagon
the number 1
what is the second rule for working out the product identities
- for two functions opposite each other
- their product is equal to 1
what is the value tan cot
tan cot = 1
what is the rule for working out reciprocal identities
a function is equal to 1 over the function opposite it
what is the reciprocal identity for cot
cot = 1 / tan
what is the rule for working out co-function identities
- by going horizontally across the hexagon in either way
- with a function = f(x) where x is an angle in degrees
- the function f(x) equals the function across it with g(90 - x)
using this rule, what does sinx equal
sinx = cos(90-x)
what does cosecx equal
cosecx = sec(90-x)
what is the first rule for working out the Pythagorean identities
- going clockwise/anticlockwise around the three inside triangles
- starting at the top, across, then ending at the bottom gives you an addition identity
- where the square of the first two functions equals the square of the last one
using this rule, what does tan^2x + 1 equal
tan^2x + 1 = sec^2x
what is the second rule for working out the pythagorean identities
- going clockwise/anticlockwise around the three inside triangles
- starting at the bottom, going up, then across gives you a subtraction identity
- where the square of the first two functions equals the square of the last one
using this rule what does 1 - cos^2x equal
1 - cos^2x = sin^2x
