MATLAB: Do I receive matrix dimensions errors when using INTEGRAL in MATLAB 7.14 (R2012a)

MATLAB

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);

Best Answer

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)
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