TRAPZ(x,y) QUAD(FH,A,B) DBLQUAD(FH,XMIN,XMAX,YMIN,YMAX) TRIPLEQUAD(FH,XMIN,XMAX,YMIN,YMAX,ZMIN,ZMAX) Creating a function handle, FH, from a function, f: 1- inline object: FH=inline(f) 2- function handle: Write a m_file with the name filename.m in the following format: function z=filename(x,y) z=f(x,y) [email protected] Trapz computes the integral of Y with respect to X using the trapezoidal method Cumtrapz computes the cumulative integral of Y with respect to X using

trapezoidal integration. x=linspace(-1,2,100); y=humps(x); format long Area=trapz(x,y) plot(x,y) grid on xlabel(x) ylabel(humps(x)) title(integral of humps) z=cumtrapz(x,y) hold on plot(x,z) hold off

Inline function: y(x) = 1./(x.^3-2*x-5) Q= -0.4605 -0.4605 Evaluates the double integral of f(X,Y) over the rectangle XMIN <= X <= XMAX, YMIN <= Y <= YMAX. f can be an inline object or a function handle. Q = dblquad(inline('y*sin(x)+x*cos(y)'), pi, 2*pi, 0, pi) or Q = dblquad(@integrnd, pi, 2*pi, 0, pi) where integrnd.m is an M-file: function z = integrnd(x, y)

z = y*sin(x)+x*cos(y); Answer: Q= -9.86960437725457 evaluates the triple integral of FUN(X,Y,Z) over the three dimensional rectangular region XMIN <= X <= XMAX, YMIN <= Y <= YMAX, ZMIN <= Z <= ZMAX. Q = triplequad(inline('y*sin(x)+z*cos(x)'), 0, pi, 0, 1, -1, 1) Answer: Q= 1.99999999436264 b

F dl a E ds s V V

dV b E dl a Q = quad(inline('-18.*sin(phi).*cos(phi)'),(pi/2),pi) Q= 8.99999998379294

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