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# Calc 113 1

### Calculus Integration part 1

Sin(x)Cos(y) 1/2(sin(x-y) + sin(x+y))
sin(x)sin(y) 1/2(cos(x-y) - cos(x+y))
cos(x)cos(y) 1/2(cos(x-y) + cos(x+y))
sin^2(x) 1-cos(2x)/2
cos^2(x) 1+cos(2x)/2
(a^2-x^2)^1/2 subst? x=asin(t)
Sin(x)Cos(y) 1/2(sin(x-y) + sin(x+y))
(a^2-x^2)^1/2 which identity do you use? 1-sin^2(t)=cos^2(t)
sin(x)sin(y) 1/2(cos(x-y) - cos(x+y))
(a^2+x^2)^1/2 which identity do you use? 1+tan^2(t)=sec^2(t)
cos(x)cos(y) 1/2(cos(x-y) + cos(x+y))
sin^2(x) 1-cos(2x)/2
cos^2(x) 1+cos(2x)/2
(x^2-a^2)^1/2 which identity do you use? sec^2(t)-1=tan^2(t)
(a^2-x^2)^1/2 subst? x=asin(t)
Intergral f'(x)g(x)dx = f(x)g(x)-integral f(x)g'(x)dx
(a^2-x^2)^1/2 which identity do you use? 1-sin^2(t)=cos^2(t)
Shell Method V=2(pi)rh(dr) V=(circumference)(height)(thickness) integral 2(pi)x(f(x))dx
(a^2+x^2)^1/2 subst? x=atan(t)
Volumes formula V=integral A(x)dx A(x)=area
(a^2+x^2)^1/2 which identity do you use? 1+tan^2(t)=sec^2(t)
(x^2-a^2)^1/2 subst? x=asec(t)
Shell Method choosing variable of integral Variable of the integral should be in the same direction as the axis of rotation x=0 is dx y=0 is dy
(x^2-a^2)^1/2 which identity do you use? sec^2(t)-1=tan^2(t)
Washer Method choosing variable of integral variable of integral should be going the opposite direction of the axis of rotation(but can be either) x=0 is dy y=0 is dx
Intergral f'(x)g(x)dx = Intergral f'(x)g(x)dx = f(x)g(x)-integral f(x)g'(x)dx
Work = ? W=fd or W=mgd work=force*distance or work=(mass*gravity)*distance
Shell Method V=2(pi)rh(dr) V=(circumference)(height)(thickness) integral 2(pi)x(f(x))dx
Work = ? (integral) W=integral f*dx
Volumes formula V=integral A(x)dx A(x)=area
Hook's Law F=kd Force=(hook's constant)(distance stretched from natural length)