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
