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31 Cards in this Set
- Front
- Back
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d/dx (sin-¹x)
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1/sqrt(1-x²)
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d/dx (sin-¹u)
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1/ (1-u²) du/dx
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d/dx (tan-¹x)
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1/ (1+x²)
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d/dx (tan-¹u)
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1/(1+u²) du/dx
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d/dx (sec-¹x)
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1/x[sqrt(x²-1)]
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d/dx(sec-¹u)
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1/[u(sqrt u²-1)]
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sin(x+y)
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sinxcosy+cosxsiny
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sin(x-y)
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sinxcosy-cosxsiny
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cos(x+y)
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cosxcosy-sinxsiny
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cos(x-y)
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cosxcosy+sinxsiny
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tan(x+y)
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tanx+tany/1-tanxtany
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sin²x
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1-cos2x/2
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tan(x-y)
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tanx-tany/1+tanxtany
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sin2x
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2sinxcosx
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cos2x
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cos²x-sin²x
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tan2x
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2tanx/1-tan²x
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sin²x
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1-cos2x/2
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cos²x
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1+cos2x/2
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tan²x
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1-cos2x/1+cos2x
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sin u/2
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±sqrt(1-cosu/2)
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cos u/2
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±sqrt(1+cosu/2)
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integral dx/[sqrt(1-x²)]
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sin-¹x + c
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integral du/[sqrt(a²-u²)]
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sin-¹u/a + c
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integral dx/(1+x²)
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tan-¹x + c
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integral du/(a²+u²)
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1/a tan-¹(u/a) + c
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integral dx/x[sqrt x²-1]
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sec-¹x + c
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integral du/u[sqrt u²-a²]
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1/a sec-¹ u/a + c
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shell
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V=2¶ integral x · f(x)dx
revolves around y |
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disk
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V=¶ integral [f(x)]²dx
revolves around x axis |
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integral of sinM x·cosN x dx
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1)N is odd: u=sinx; du=cosxdx
cos²x=1-sin²x 2)M is odd: u=cosx; du=-sinxdx sin²x=1-cos²x 3)M and N are even: sin²x=1-cos2x/2 cos²x=1+cos2x/2 |
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integral tanM x ·secN x dx
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1)N is even: u=tanx; du=sec²x
sec²x=1+tan²x 2)M is odd: u=secx: du=secxtanxdx tan²x=sec²x-1 |
