Integration/differentiation Flashcards
(19 cards)
What is the integral of Sec^2x
tanx
What is the integral of cosecxcotx
-cosecx
What is the integral of cosec^2x
-cotx
What is the integral of secxtanx
secx
How do we integrate this parametrically
How do we differentiate 2xy with respect to x
Split x’s & ys and apply product rule
ie
2x x y
What is the formula for parametric integration
What’s the formula for integration by parts
Prove the derivative of cosx is -sinx
What is the first principles equation
f(x+h) - f(x)/h
Prove the derivative of sinx is cosx
What do we do when integrating if we want to flip the bounds (if top is smaller than bottom)
We put a minus in front of the function and flip
What’s the pneumonic to remember order of priority of what is U and what is V’ when integrating by parts
IF ITS A LOGARITHM, ITS U, IF NO LOG THEN ITS THE ALGEBRAIC TERM (x term) FOR U
🧠 How to Choose
𝑢 and 𝑑𝑣
A useful rule is LIATE:
Logarithmic, Inverse trig, Algebraic, Trigonometric, Exponential.
(We don’t integrate inverse trig functions in a level maths so the rule to remember is LOG TAKES PRIORITY FOR U)
What is the first principles equation
f(x+h) - f(x)/h
What’s the derivative of
What’s the derivative of
If second derivative is 0, what do we do to confirm the nature of the stationary point
If second derivative is negative –> Local MAX
If second derivative is positive —> Local MIN
If second derivative is 0:
Check SECOND DERIVATIVE either side of x value:
Changes sign either side (from + to – or – to +) then point of inflection
Negative and negative –> May be a Local MAX but have to check first derivative: Positive to negative means MAX
Positive to positive —> May be a Local MIN but have to check first derivative: Negative to positive means MIN
