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integral of tanxdx
lncosx+c

integral (cotxdx)
lnsinx+c

integral secxdx
lnsecx+tanx+c

integral of cscxdx
lncscx+cotx+c

integral of sin^2xdx
integral of (1cos2x)/2 dx

integral of cos^2xdx
integral of (1+cos2x)/2 dx

integral of tan^2x
tan(x)x+c

integral of cot^2x
xcot(x)+c

integral of lnxdx
xlnxx+c

integral of (1/x)dx
lnx+c


derivative of tan^1x
1/(x^2+1)

derivative of sin^1x
1/sqrt(1x^2)

derivative of cos^1x
1/sqrt(1x^2)

Fundamental Theorem of Calc Part 2
if f(x) is continuous on an open itnerval containing a, then for every x in the interval:
d/dx(integral of [f(t)dt] (a,x))=f(x)

Fundamental Theorem of Calc
if a function is continuous on [a,b] and F is an antideriv of f(x) then
integral of f(x)dx (a,b) = F(b) F(a)

average value of a function
Avg Val= 1(ba) * integral f(x)dx (a,b)

mvt for integrals
integral of f(x)dx (a,b)=(ba)*f(c)

equilateral triangle
A=(S^2(rad3))/4

rhombus (area)
a=.5 (d1*d2)

area of trapezoid
A=.5h(b1+b2) OR A=hm (m is the midsegment)

regular polygon
A= .5a (apothem)p (perimeter)

SA of pyramids
A= .5pl + b

volume of cone/ sa of cone
(1/3)pir^2h/ pi(r)(l)+(pi)r^2

rate of change is proportional / inversely
dy/dt=ky ; k/y

growth/decay
A= Ao e^(kt)

find y1
y0 + h times F(x0, y0)

revolve aroudn y
V= integral of pi (f(y))^2 dy (a to b)

revolve around x
V= integral of pi (f(x))^2 dx (a to b)

cross section
integral of (f(x)  g(x))^2 dx from to b

arc length
integral from a to b of square root of (1+ f'(x)^2) dx

