Create the function $$f(x)=e^{-x^2}(\ln x{)}^2$$.

fun = @(x) exp(-x.^2).*log(x).^2;

Evaluate the integral fromx=0tox=Inf.

q = integral(fun,0,Inf)

q = 1.9475

Create the function $$f(x)=1/(x^3-2x-c)$$with one parameter, $$c$$.

fun = @(x,c) 1./(x.^3-2*x-c);

Evaluate the integral fromx=0tox=2atc=5.

q = integral(@(x) fun(x,5),0,2)

q = -0.4605

SeeParameterizing Functionsfor more information on this technique.

Create the function $$f(x)=\ln (x)$$.

fun = @(x)log(x);

Evaluate the integral fromx=0tox=1with the default error tolerances.

formatlongq1 = integral(fun,0,1)

q1 = -1.000000010959678

Evaluate the integral again, this time with 12 decimal places of accuracy. SetRelTolto zero so thatintegralonly attempts to satisfy the absolute error tolerance.

q2 = integral(fun,0,1,'RelTol',0,'AbsTol',1e-12)

q2 = -1.000000000000010

Create the function $$f(z)=1/(2z-1)$$.

fun = @(z) 1./(2*z-1);

Integrate in the complex plane over the triangular path from0to1+1ito1-1ito0by specifying waypoints.

q = integral(fun,0,0,'Waypoints',[1+1i,1-1i])

q = -0.0000 - 3.1416i

Create the vector-valued function $$f(x)=[\sin x,\sin 2x,\sin 3x,\sin 4x,\sin 5x]$$和中国ate fromx=0tox=1. Specify'ArrayValued',trueto evaluate the integral of an array-valued or vector-valued function.

fun = @(x)sin((1:5)*x); q = integral(fun,0,1,'ArrayValued',真正的)

q =1×50.4597 0.7081 0.6633 0.4134 0.1433

Create the function $$f(x)=x^5{e}^{-x}\sin x$$.

fun = @(x)x.^5.*exp(-x).*sin(x);

Evaluate the integral fromx=0tox=Inf, adjusting the absolute and relative tolerances.

formatlongq = integral(fun,0,Inf,'RelTol',1e-8,'AbsTol',1e-13)

q = -14.999999999998360