Integration
by parts
by parts
The order of the five different functions used when integrating by parts
What is Log Functions, Inverse Trig Functions, Polynomials, Exponentials, Trig Functions
The formula for finding the length of a rectangular curve
What is the integral from a to b of the square root of 1 + (dy/dx)^2
The Parametric Differentiation Formula.
What is (dy/dt)/(dx/dt)?
The formulas used for converting polar coordinates to rectangular coordinates
What are
x = rcosθ
y = rsinθ
The Taylor Series for sin(x) centered at x=0?
What is
x-x^3/3! + x^5/5! - x^7/7! + ... (-1)^n x^2n+1/(2n+1)!
The formula for solving all integration by parts problems
what is
uv - ∫vdu
The length of the curve
y=⅓(x^2 + 2)^3/2 from x=0 to x=3
What is 12?
The formula for finding parametric speed
What is the integral of the square root of x'(t)^2 + y'(t)^2
The shape of the polar curve
r=2cos(3θ)
y=2cos(3x)
What is a rose curve?
The first three nonzero terms of the Maclaurin Series of Sin(x^2).
What is x^2-x^6/3!+x^10/5!?
The solution to ∫2x(arctan(x)) dx
What is
x^2(arctan(x)) - x + arctan(x) + C
The length of the curve
y=25cos(pi x/50) from 0 to 25
What is 57.622?
Integral for Length of the parametric curve of
x=cos^3(t), y=sin^3(t)
What is the integral of the square root of 9cos^4(t)sin^2(t) + 9sin^4(t)cos^2(t) dt
The rectangular expression for
r = 4/(3cosθ)
What is x=4/3
The second degree Taylor polynomial of f(x)=1/(x+2) at x=-1.
What is 1-(x+1)+(x+1)^2/2!?
The solution to ∫x^2*e^3x dx
What is (1/3)x^2(e^3x) - (2/9)xe^3x + (2/27)e^3x + C
The length of the parametric curve
x=1/3t^3 y=1/2t^2
What is (2√2 - 1)/3
The area under the parametric curve 0 to 2pi
x=2cos(t), y=3sin^2(t)
What is 0
The slope of the line tangent to the polar curve r=1+2sinθ at θ=0
What is 1/2
f^20(0) of the Taylor series
2x + 3x^2 + 4/2!x^3 + 5/3!x^4 + ... (n+1)/(n-1)!x^n
What is 420?
The solution to ∫sin(3x)cos(5x) dx
What is cos(2x)/4-cos(8x)/16+ C
The length of the parametric curve
x=2cos^3(t) y=2sin^3(t) from 0 to 2pi
What is 12?
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 area of the region enclosed by the polar curve r=sin(2θ) for 0 ≤ θ ≤ pi/2
What is pi/8
The power series 1-x^2/3!+x^4/5!-x^6/7! converges to
What is sinx/x?