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Log -> Inv Trig -> Algebraic -> Trig -> Expontential

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Log -> Inv Trig -> Algebraic -> Trig -> Expontential

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Good to look to use when there is a washer problem in respect to y

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Good to look to use when there is a washer problem in respect to y

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Square: A(x) = (top - bottom)^2
Equilateral Triangle: A(x) = sqroot(3)/4(top - bottom)^2
Semi-Circle: A(x) = 1/2pi ((top - bottom)/2)^2

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sqrt 1 + (f(x)prime)

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2 pi sqrt 1+ (f(x)prime)

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divergent

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convergent

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S = 2pi integral r(x) sqrt(1 + dx/dyf(x)^2) dx

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Improper if the integral has a discontinuity or goes to plus/minus infinity

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sqrt(a^2 + u^2)
u=atan(x)

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sqrt(u^2 - a^2)
u=asec(x)

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Linear Root: a/(mx+b)

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sqrt(a^2 - u^2)
u=asin(x)

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L = integral sqrt(1 + dx/dyf(x)^2) dx

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Repeated Linear Root: (a/(mx+b))+(b/(mx+b)^n)

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Irreducible Quadratic: (ax+b)/(a(x^2)+bx+c)

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Divergent if there if infinity or negative infinity

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Convergent if limit exists

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Repeated Irreducible Quadratic: ((ax+b)/(a(x^2)+bx+c))+((cx+d)/(a(x^2)+bx+c))

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The limit of the sequence is the value of the sequence as n approaches infinity

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P-test

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Geometric series (and their expressions) to evaluate convergence

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Integral Test

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Direct Comparison Test

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Limit Comparison Test

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Ratio Test

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Root Test