C4- Integration Flashcards
∫(1/x)dx
ln|x| + c
∫sinx dx
-cosx +c
∫cosx dx
sinx +c
∫tanx dx
ln|secx| +c
∫cotx dx
ln|sinx| +c
∫secx dx
ln|secx + tanx| +c
∫cosecx dx
-ln|cosecx + cotx| +c
∫sec^2(x) dx
tanx +c
∫-(cosecx)(cotx) dx
cosecx +c
∫(secx)(tanx) dx
secx +c
∫-cosec^2(x) dx
cotx +c
∫(f’(x))/(f(x)) dx
ln|f(x)| +c
∫f(x)[f(x)]^n dx
[1/n+1][f(x)]^(n+1)
What is the formula for integrating by parts?
∫u(dv/dx) dx = uv - ∫v(du/dx) dx
What is the formula for the volume of revolution around the x-axis between x=a and x=b?
π∫ (y^2 dx)
How do you separate the variables of: dy/dx=[f(x)][g(y)]?
∫(1/g(y)) dy = ∫f(x) dx
What is the trapezium rule?
∫y dx= (1/2)(h)[y0 + yn + 2(y1+y2+y3+…+yn-1)]
where h=(b-a)/n
∫1/(ax+b) dx
(1/a)(ln|ax+b|) +c
∫cos(ax+b) dx
(1/a)(sin(ax+b)) +c
∫sin(ax+b) dx
-(1/a)(cos(ax+b)) +c
∫sec^2(ax+b) dx
(1/a)(tan(ax+b)) +c
∫cosec(ax+b)cot(ax+b) dx
-(1/a)(cosec(ax+b)) +c
∫cosec^2(ax+b) dx
-(1/a)(cot(ax+b)) +c
∫sec(ax+b)tan(ax+b) dx
(1/a)(sec(ax+b)) +c
