Final Prep Flashcards
(23 cards)
What is the derivative of tanx
sec^2X
What is the derivative of sinx
cosx
What is the derivative of cosx
-sinx
What is the integral of sec^2x
tanx
What is the integral of sinx
-cosx
What is the integration by parts formula
uv-integral(vdu)
What is the integral of cosx
sinx
In trigonometric integrals when the exponent of sin is odd and positive and the exponent of cos is a real number
split off a sinx and u = cosx
In trigonometric integrals when the exponent of cos is odd and positive and the exponent of sin is a real number
split off a cosx and u = sinx
sin^2x =
1 - cos^2x
cos^2x =
1 - sin^2x
Half angle formula for sin^2x
1/2(1-cos2x)
In trigonometric integrals when the exponent of sin and cos are both even and non negative
Use the half angle formulas
Half angle formula for cos^2x
1/2(1+cos2x)
If an integral contains a^2 - x^2
x = asin(theta)
If an integral contains a^2 + x^2
x = atan(theta)
If an integral contains x^2 - a^2
x = asec(theta)
Integral of a/x
a/dx ln(x) + C
Formula for pumping problems
pg * Integral( D(y)*A(y) dy )
Formula for lifting problems
pg * Integral( D(y) dy )
Formula for spring problems
Integral( kx dx )
In power series if the limit converges to 0
Radius is infinity and Interval of Convergence is negative infinity to positive infinity
In a power series if the limit converges to infinity
Radius is zero and Interval of Convergence is a single point, the number that is being subtracted from x
