Riemann Sums
This type of Riemann sum approximation uses the function value at the leftmost point of each subinterval to determine the height of the rectangles.
What is a Left Riemann Sum?
In the arc length formula, this is where can you find the specific interval [a,b].
THis technique slices a 3-D solid into ______ thin shapes and sums their volumes.
What is 'infinitely'?
This formula for volumes of revolution contains the multiple of 2pi on the integral.
What is the Shell method?
Area formula for a square cross section (in terms of s).
A=s^2
Among the left, right, and midpoint methods, this specific Riemann sum generally provides the most accurate approximation of the definite integral.
What is the Midpoint Sum?
In the Area between curves formula, in association with y, this is what function you subtract from the other. (Ex: in terms of x you subtract the top function from the bottom function)
What is the Right function - the Left function?
For a solid whose base is bounded by f(x) and g(x) (where f(x) > g(x)), this is the area expression for the cross section that is a square.
What is [f(x)-g(x)]^2?
This method is used when rotating two functions (perpendicular to the axis of rotation of course).
What is the Washer method?
The arc length formula.
What is the integral from a to b of sqrt(1+[f'(x)]^2)dx?
When using a trapezoidal Riemann sum, the trapezoid must touch the curve that you're approximating with both of these.
What are the (top) vertices?
The area of the region bounded by y=x^2 and y=x+2 between x=-1 and x=2.
What is 9/2?
When cross sections are semicircles with diameters stretching across the base s(x), this is the resulting area function (A(x)).
What is (pi/2)((s(x)/2)^2)?
OR
What is (pi/8) ([s(x)]^2)?
If the region bounded by y=sin(x) and the x-axis from x=0 to x=pi is revolved around the line y=-1, the expression for the outer radius R(x) in the Washer method is this.
What is sin(x) +1?
Area formula for an equilateral triangle cross section (in terms of s).
A= (sqrt(3)/4) s^2