Integration P2 Flashcards
what is the integration of cosecx cotx
-cosecx + c
what is the integration of secx tanx
secx + c
what is the integration of cosec^2x
-cotx + c
what is the integration of cosec(ax+b) cot(ax+b)
-1/a cosec(ax+b) + c
what is the integration of sec(ax+b) tan(ax+b)
1/a sec(ax+b) + c
what is the integration of cosec^2(ax+b)
-1/a cot(ax+b) + c
what is the double angle formula for sin2A
sin2A = 2(sinA cosA)
what is the double angle formula for cos2A
cos2A = cos^2A - sin^2A
what is the double angle formula for tan2A
tan2A = (2tanA) / (1 - tan^2A)
just as a quick reminder, what do i mean by sin^2A
(sinA)^2
what does the integration of f’(x) / f(x) equal
ln(|f(x)| + c)
what does ln(|f(x)| + c) equal when a k rather than a c where the c is basically the k
- ln|f(x)| + lnk
- ln(k * |f(x)|)
what is the integration of tan kx
1/k ln|sec kx| + c
what is the integration of cosecx
-ln[cosecx + cotx] + c
what is the integration of secx
ln[secx + tanx] + c
what is the integration of cotx
ln[sinx] + c
what would the integration of any of these (kx) functions be
1/k ln{ whatever this is (kx)] + c
What is the formula for parametric integration
Integration of y (dx) = integration of y * dx/dt (dt)
what is the integration of f’(x) / f(x)
- ln |f(x) + c|
- which = ln |k * f(x)|
what is the formula for integration by parts
int (uv’) = uv - in (vu’)
how do you find f(u) from the int (du/dx f’(u))
du/dx * int(f’(u)) = f(u) + c
what is the equation for int(y) dx with parametric equations
- int(y) dx = int(y * dx/dt) dt
- your y and dx/dt are in terms of y so multiply them and int with respects to t
- you will need to convert limits in terms of t if needed
what is the small angle approximation of sin0
sin0 = 0
what is the small angle approximation of cos0
cos0 = 1 - (1/2 0^2)
what is the small angle approximation of tan0
tan0 = 0
