integrals Flashcards
x^n
(x^n+1)/(n+1) + C
1/x
ln|x| + C
u’/u
ln|u| + C
e^x
e^x + C
a^x
a^x/lna + C
cosx
sinx + C
sinx
-cosx + C
sec^2 x
tanx + C
tanx
-ln|cosx| + C
u’/(a^2+u^2)
(1/a)arctan(u/a) + C
u’/(a^2-u^2)^1/2
arcsin(u/a) + C
cotx
ln|sinx| + C
secxtanx
secx + C
csc^2 x
-cotx + C
cscxcotx
-cscx + C
volume of a disc
V=pi%r^2
integral is b%a
volume of a washer
V=pi%(R^2-r^2)
integral is b%a
volume of a cross section
V=%A
integral is b%a
fundamental theorem
%f’(x)dx=f(b) - f(a)
integral is b%a
start plus accumulation
f(b)=f(a) + %f’(x)dx
integral is b%a
second fundamental theorem
(d/dx)%f(t)dt=f(v)v’ - f(u)u’
integral is v%u
area of trapezoid
A=(1/2)w(h1+h2)
riemann sum
add areas of rectangles
average value of a function
favg=(%f(x)dx)/(b-a) (avg height=area/width
integral is b%a
displacement
%v(t)dt
integral is t2%t1
total displacement
%|v(t)|dt
integral is t2/t1
