Why do I receive matrix dimensions errors when using INTEGRAL in MATLAB 7.14 (R2012a)?

When using the INTEGRAL command as follows,

integral(@(x) x^2,0,100)

I receive an error:

 Error using  ^ 

 Inputs must be a scalar and a square matrix.

 To compute elementwise POWER, use POWER (.^) instead.

 Error in @(x)x^2

 Error in integralCalc/iterateScalarValued (line 314)

                 fx = FUN(t);

 Error in integralCalc/vadapt (line 133)

             [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

 Error in integralCalc (line 76)

         [q,errbnd] = vadapt(@AtoBInvTransform,interval);

 Error in integral (line 89)

 Q = integralCalc(fun,a,b,opstruct);

This issue also occurs when I multiply "x" in functions such as "x*sin(x)". Additionally, I get another type of error when using divisions:

integral(@(x) x/exp(x),0,100)

 Error using integralCalc/finalInputChecks (line 515)

 Output of the function must be the same size as the input. If FUN is

 an array-valued integrand, set the 'ArrayValued' option to true.

 Error in integralCalc/iterateScalarValued (line 315)

                 finalInputChecks(x,fx);

 Error in integralCalc/vadapt (line 133)

             [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

 Error in integralCalc (line 76)

         [q,errbnd] = vadapt(@AtoBInvTransform,interval);

 Error in integral (line 89)

 Q = integralCalc(fun,a,b,opstruct);

Answer 1

[MathWorks Support Team]

The first error indicates that the matrix dimensions do not agree. This is because the INTEGRAL command passes the value of "x" into the function argument as a vector. However, since the "^" operator tries to square this vector, the matrix dimensionality error occurs. This is same as trying:

[1 2 3]^2

For divisions, the vectors involved in the division undergo matrix division and yield a scalar. However, the output that is expected by INTEGRAL is a vector. Therefore, although there is no error when calculating the division, an error occurs while evaluating the integral.

To work around these issues, please use element-wise math operators in the function definition. The correct commands would be:

integral(@(x) x.^2,0,100)

integral(@(x) x./2,0,100)