Integrals
∫cotxcscxdx=
What is -cscx+c
The Parametric Differentiation Formula.
What is (dy/dt)/(dx/dt)?
Evaluate the sum from i = 1 to 5
Σ (5i + 2)
85
The formula for area between 2 curves
What is ∫[f(x)−g(x)]dx
The formula for solving all integration by parts problems
what is
uv - ∫vdu
∫(3/x)dx=
What is 3lnlxl+c
The shape of the polar curve
r=2cos(3θ)
What is a rose curve?
The first three non-zero terms of the maclaurin series of sinx
What is x-x3/3!+x5/5!
The area of the region bounded by f(x)=x2+2x+1 and g(x)=2x+5
What is 10.667
By expanding a function into an infinite polynomial using derivatives, this mathematician was able to estimate values from it.
Who was Taylor?
∫1/(x2+4x+3)dx=
What is (1/2)(lnl(x+1)/(x+3)l)+c
The rectangular expression for
r = 4/(3cosθ)
What is x=4/3
This is the specific type of series you get when p=1.
What is harmonic series?
The area of the region bounded by f(x)=x2 and g(x)=6-x
What is 20.833
The Trapezoidal approximation using n trapezoids is calculated by:
(b-a)/2n * ( f(x_0) + 2*f(x_1) + 2*f(x_2) + ... + 2*f(x_n-1) + f(x_n))
Find T4 for f(x) = sin(x) on the interval [0,pi].
pi(1+sqrt(2))/4
approx 1.896
∫arctanxdx=
What is xarctanx-(1/2)(lnl1+x2l)+c
The slope of the line tangent to the polar curve r=1+2sinθ at θ=0
What is 1/2
This test requires replacing all n's with n+1, then dividing tat by the original and then taking the limit to infinity.
What is the ratio test?
The area of the region enclosed by r=3(1+cos(θ))
What is 27pi/2
The general solution to
y' = 2y + 1.
What is y = Ce2x − 1/2?
∫xexdx=
What is xex-ex+c
The second derivative of the parametric equation
x= t^3 - 6t^2 + 9t + 1, y= 2t^3 - 9t^2 - 2
What is -2/((t-1)^2(3t^2-12t+9))
The first four terms of the series: 1/(1+x^3)
What is 1-x^3+x^6-x^9+...
Find the volume of the solid generated by revolving the region bounded by y=x2, the x-axis, and x=2 around the x-axis.
What is 32π/5?
The length of the parametric curve
x=2cos^3(t) y=2sin^3(t) from 0 to 2pi
What is 12?