MATLAB Mathematics - SERC - Index of

4 Function Functions
A three-dimensional plot of this curve is
t = 0:0.1:3*pi;
plot3(sin(2*t),cos(t),t)
The arc length formula says the length of the curve is the integral of the norm
of the derivatives of the parameterized equations
3π
∫
0
2
4cos( 2t)
The function hcurve computes the integrand
function f = hcurve(t)
f = sqrt(4*cos(2*t).^2 + sin(t).^2 + 1);
Integrate this function with a call to quad
len = quad(@hcurve,0,3*pi)
len =
1.7222e+01
2
+ sin( t)
+ 1 dt
The length of this curve is about 17.2.
Example: Double Integration
Consider the numerical solution of
ymax
∫
ymin
xmax
∫
xmin
fxy ( , ) dxdy
For this example fxy ( , ) = ysin( x)
+ xcos( y)
. The first step is to build the
function to be evaluated. The function must be capable of returning a vector
output when given a vector input. You must also consider which variable is in
the inner integral, and which goes in the outer integral. In this example, the
inner variable is x and the outer variable is y (the order in the integral is dxdy).
In this case, the integrand function is
function out = integrnd(x,y)
out = y*sin(x) + x*cos(y);
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