# math

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } integral of tanxdx -ln|cosx|+c integral (cotxdx) ln|sinx|+c integral secxdx ln|secx+tanx|+c integral of cscxdx -ln|cscx+cotx|+c integral of sin^2xdx integral of (1-cos2x)/2 dx integral of cos^2xdx integral of (1+cos2x)/2 dx integral of tan^2x tan(x)-x+c integral of cot^2x -x-cot(x)+c integral of lnxdx xlnx-x+c integral of (1/x)dx ln|x|+c derivative of lnx 1/x derivative of tan^-1x 1/(x^2+1) derivative of sin^-1x 1/sqrt(1-x^2) derivative of cos^-1x -1/sqrt(1-x^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 anti-deriv of f(x) then integral of f(x)dx (a,b) = F(b)- F(a) average value of a function Avg Val= 1(b-a) * integral f(x)dx (a,b) mvt for integrals integral of f(x)dx (a,b)=(b-a)*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 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Authorxtonyfl ID42104 Card Setmath Descriptionlul Updated2010-12-10T07:56:34Z Show Answers