Integrals

Riemann Sums

To estimate a definite integral of a function with a Riemann sum over an interval $[a,b]$,

riemannSum(f,a,b)

Arc Length

To get the length of some explicit curve over an interval $[a,b]$,

arcLength(f,a,b)

Area Bounded by Two Functions

To get the area between two functions over an interval $[a,b]$,

areaBounded(f,g,a,b)

Volume of Revolution

To get the volume of a solid resulting from the revolution of a function $f(x)$ about some axis $g(x)$ over the interval $[a,b]$,

volumeOfRevolution(f,g,a,b)

Volume of a Shell

To get the volume of a shell resulting from the revolution of a function $f(x)$

shellRevolution(f,a,b)

Line integrals

To get the volume of a parametric curve $c = (g_1(x_1),g_2(x_2),\dots,g_n(x_n))$ over some scalar function $f(x_1,x_2,\dots,x_n)$, over an interval $[a,b]$,

lineIntegral(f,c,a,b)

Rectangular double integrals

To get the volume of a scalar function $f(x_1,x_2)$ over some rectangular region $\omega = [a,b] \times [c,d]$,

doubleIntegral(f,((a,b),(c,d)))