Integration year 2 Flashcards
How do you integrate x^n?
x^(n+1) /n+1 +c
How do you integrate e^x?
e^x + c
How do you integrate 1/x?
Ln|x| + c
What is the integration order of sin and cos?
-cos -> -sin —> cos —> sin
What is sec^2x integrated?
tanx + c
What is cosecxcotx integrated?
-cosecx + c
What is cosec^2x integrated?
-cotx +c
What is secxtanx integrated?
Secx + c
How do you do the reverse chain rule?
- Add 1 to the power
- Differentiate
- Simplify
- Work out how many bigger than the original
- Solve
What does the integral of f’(ax + b) equal?
1/a f(ax + b) + c
How do you integrate tan^2x?
change to sec^2x - 1
then that integrates to tanx - 1 + c
How do you integrate sin^2x?
change to 1/2 - 1/2cos2x
then that integrates to 1/2x - 1/4sin2x + c
How do you integrate by subsitution?
rearrange for u
differentiate u and rearrange for dx
sub into the equation
integrate
sub x back in
What do you do to the limits if you integrate by substitution?
you sub the values in as x and solve to find the limits of u
What is the formula for integrating by parts? (multiplied)
|u dv/dx = uv - |v du/dx
What is the order of what becomes u in integration?
LATE:
Logarithms
Algebra
Trig
Exponentials
How many times can you integrate by parts for the same integration?
twice
How do you integrate fractions?
Covert into partial fractions and integrate them
How do you integrate fractions when the order of the numerator is equal to or greater than the denominator?
use algebra long division to turn into 1 + a fraction
then turn that fraction into partial fractions
