Calculus 2 Formula Sheet

On this page, I plan to accumulate all of the math formulas that will be important to remember for Calculus 2.

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The Area of a Region Between Two Curves

Suppose that f and g are continuous functions with f(x) ≥ g(x) on the interval [a, b]. The area of the region bounded by the graphs of f and g on [a,b] is:

Area of a Region Between Two Curves with Respect to y

Suppose that f and g are continuous functions with f(y) ≥ g(y) on the interval [c, d]. The area of the region bounded by the graphs x = f(y) and x = g(y) on [c, d] is:

General Slicing Method

Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is:

Disk Method about the X Axis

Let f be continuous with f(x) ≥ 0 on the interval [a, b]. If the region R bounded by the graph of f, the x-axis, and the lines x = a and x = b is revolved about the x-axis, the volume of the resulting solid of revolution is:

Area of circle = πr².

You get r from measuring the distance of f(x) to the x-axis.

dx is the thickness or width of the disk.

∫ for interval [a, b] is a summation of all the disks between [a, b].

Washer Method about the x-axis

Let f and g be continuous functions with f(x) ≥ g(x) ≥ 0 on [a, b]. Let R be the region bounded by the curves y = f(x) and y = g(x), and the lines x = a and x = b. When R is revolved about the x-axis, the volume of the resulting solid of revolution is

Volume by the Shell Method

Let f and g be continuous functions with f(x) ≥ g(x) on [a, b]. If R is the region bounded by the curves y = f(x) and y = g(x) between the lines x = a and x = b, the volume of the solid generated when R is revolved about the y-axis is:

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