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cueFlash >Decks >Calc Ii Exam 1 >Glossary  

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Glossary of calc ii exam 1

Created by 35173

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(cos(x))^2

(1/2)(1+cos(2x)) OR 1-(sin(x))^2

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Card Front(cos(x))^2

Card Back(1/2)(1+cos(2x)) OR 1-(sin(x))^2

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(csc(x))^2

1+ (cot(x))^2

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Card Front(csc(x))^2

Card Back1+ (cot(x))^2

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(sin(x))^2

(1/2)(1-cos(2x)) OR 1-(cos(x))^2

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Card Front(sin(x))^2

Card Back(1/2)(1-cos(2x)) OR 1-(cos(x))^2

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(tan(x))^2

(sec(x))^2 -1

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Card Front(tan(x))^2

Card Back(sec(x))^2 -1

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arc length formula

L = ~sqrt(1+(f'(x))^2) dx

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Card Frontarc length formula

Card BackL = ~sqrt(1+(f'(x))^2) dx

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a^2 - x^2

u = sin^(-1)(x/a)

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Card Fronta^2 - x^2

Card Backu = sin^(-1)(x/a)

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conditions for integrating ~(sin(x))^m(cos(x))^n dx

1. Either n or m (or both) is an odd, positive interger
2. Both m and n are non-negative even intergers

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Card Frontconditions for integrating ~(sin(x))^m(cos(x))^n dx

Card Back1. Either n or m (or both) is an odd, positive interger 2. Both m and n are non-negative even intergers

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conditions for integrating ~(tan(x))^m(sec(x))^n dx

1. m is an odd, positive interger
2. n is an even, non-negative interger

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Card Frontconditions for integrating ~(tan(x))^m(sec(x))^n dx

Card Back1. m is an odd, positive interger 2. n is an even, non-negative interger

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cos(2x)

cos(x)^2-sin(x)^2

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Card Frontcos(2x)

Card Backcos(x)^2-sin(x)^2

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Dx cos^(-1)(x)

-1/(sqrt(1-x^2))

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Card FrontDx cos^(-1)(x)

Card Back-1/(sqrt(1-x^2))

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Dx cot^(-1)(x)

-1/(1+x^2)

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Card FrontDx cot^(-1)(x)

Card Back-1/(1+x^2)

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Dx csc^(-1)(x)

-1/(|x|sqrt(x^2)-1)

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Card FrontDx csc^(-1)(x)

Card Back-1/(|x|sqrt(x^2)-1)

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Dx sec^(-1)(x)

1/(|x|sqrt(x^2)-1)

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Card FrontDx sec^(-1)(x)

Card Back1/(|x|sqrt(x^2)-1)

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Dx sin^(-1)(x)

1/(sqrt(1-x^2))

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Card FrontDx sin^(-1)(x)

Card Back1/(sqrt(1-x^2))

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Dx tan^(-1)(x)

1/(1+x^2)

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Card FrontDx tan^(-1)(x)

Card Back1/(1+x^2)

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Integration by parts

~udv = uv - ~vdu

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Card FrontIntegration by parts

Card Back~udv = uv - ~vdu

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Separate (x^2+2)/(x^3)(x-2)^2(x^2+1) into partial fractions

(a/(x))+(b/(x^2))+(c/(x^3))+(d/(x-2))+(e/(x-2)^2)+((fx+g)/(x^2+1))

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Card FrontSeparate (x^2+2)/(x^3)(x-2)^2(x^2+1) into partial fractions

Card Back(a/(x))+(b/(x^2))+(c/(x^3))+(d/(x-2))+(e/(x-2)^2)+((fx+g)/(x^2+1))

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separate x/((x+1)^2) into partial fractions

(a/(x+1)) + (b/(x+1)^2))

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Card Frontseparate x/((x+1)^2) into partial fractions

Card Back(a/(x+1)) + (b/(x+1)^2))

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simplified integration by parts

~(polynomial)(e^x, sin(x), cos(x))
differentiate each separately, then combine crosswise, alternating between positive and negative starting with negative

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Card Frontsimplified integration by parts

Card Back~(polynomial)(e^x, sin(x), cos(x)) differentiate each separately, then combine crosswise, alternating between positive and negative starting with negative

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sin(2x)

2sin(x)cos(x)

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Card Frontsin(2x)

Card Back2sin(x)cos(x)

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Surface area of f(x) around x-axis

SA = ~2(pi)f(x)sqrt(1+(f'(x))^2) dx (a, b on x-axis)

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Card FrontSurface area of f(x) around x-axis

Card BackSA = ~2(pi)f(x)sqrt(1+(f'(x))^2) dx (a, b on x-axis)

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Surface area of f(x) around y-axis

SA = ~2(pi)(x)sqrt(1+(f'(x))^2) dx (a, b, on x-axis)

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Card FrontSurface area of f(x) around y-axis

Card BackSA = ~2(pi)(x)sqrt(1+(f'(x))^2) dx (a, b, on x-axis)

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Surface area of g(y) around x-axis

SA = ~2(pi)(y)sqrt(1+(g'(y))^2) dy (a, b, on y-axis)

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Card FrontSurface area of g(y) around x-axis

Card BackSA = ~2(pi)(y)sqrt(1+(g'(y))^2) dy (a, b, on y-axis)

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Surface area of g(y) rotated around y-axis

SA = ~2(pi)g(y)sqrt(1+(g'(y))^2) dy (a, b on y-axis)

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Card FrontSurface area of g(y) rotated around y-axis

Card BackSA = ~2(pi)g(y)sqrt(1+(g'(y))^2) dy (a, b on y-axis)

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volume generated by revolving f(x) and g(x) around x-axis

v = ~(pi)[f(x)^2-g(x)^2] dx (a, b on x-axis)

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Card Frontvolume generated by revolving f(x) and g(x) around x-axis

Card Backv = ~(pi)[f(x)^2-g(x)^2] dx (a, b on x-axis)

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volume generated by revolving f(x) around y-axis

v = ~2(pi)x(f(x)) dx (a, b on x-axis)

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Card Frontvolume generated by revolving f(x) around y-axis

Card Backv = ~2(pi)x(f(x)) dx (a, b on x-axis)

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volume generated by revolving g(y) around x-axis

v = ~2(pi)y(g(y)) dx (a, b on y-axis)

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Card Frontvolume generated by revolving g(y) around x-axis

Card Backv = ~2(pi)y(g(y)) dx (a, b on y-axis)

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volume generated by rotating f(x)around x-axis

v = ~(pi)f(x)^2 dx (a, b on x-axis)

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Card Frontvolume generated by rotating f(x)around x-axis

Card Backv = ~(pi)f(x)^2 dx (a, b on x-axis)

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volume generated by rotating g(y) around y-axis (dish)

v = ~(pi)g(y)^2 dy (a, b on y-axis)

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Card Frontvolume generated by rotating g(y) around y-axis (dish)

Card Backv = ~(pi)g(y)^2 dy (a, b on y-axis)

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x^2 + a^2

u = tan^(-1)(x/a)

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Card Frontx^2 + a^2

Card Backu = tan^(-1)(x/a)

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x^2 - a^2

u = sec^(-1)(x/a)

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Card Frontx^2 - a^2

Card Backu = sec^(-1)(x/a)

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~cos(kx) dx

(1/k)sin(kx) + C

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Card Front~cos(kx) dx

Card Back(1/k)sin(kx) + C

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~cot(x) dx

ln|sin(x)| + C OR -ln|csc(x)| + C

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Card Front~cot(x) dx

Card Backln|sin(x)| + C OR -ln|csc(x)| + C

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~csc(x) dx

-ln|csc(x) + cot(x)| + C

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Card Front~csc(x) dx

Card Back-ln|csc(x) + cot(x)| + C

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~sec(x) dx

ln|sec(x) + tan(x)| + C

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Card Front~sec(x) dx

Card Backln|sec(x) + tan(x)| + C

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~sin(kx) dx

(-1/k)cos(kx) + C

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Card Front~sin(kx) dx

Card Back(-1/k)cos(kx) + C

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~tan(x) dx

-ln|cos(x)| + C OR ln|sec(x)| + C

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Card Front~tan(x) dx

Card Back-ln|cos(x)| + C OR ln|sec(x)| + C

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