MATLAB: Vectorization and plotting user-defined function

Question

I am new to MATLAB and am having trouble understanding how to plot userdefined functions.

I have defined a function f via

fun=@(t,r)(t.^2-t.^4).*exp(r.*t.^2);
fun1=@(t,r)exp(r.*t.^2);
f=@(r)integral(@(t)fun(t,r),0,1)./integral(@(t)fun1(t,r),0,1);

Now if I specify say

r=linspace(-10,10);

and type

x=f(r);

I get errors such as

Matrix dimensions must agree.
Error in @(t,r)(t.^2-t.^4).*exp(r.*t.^2)

whereas

x=sin(r);

is accepted. I seem to have been careful to use .* etc. What is the difference between my f and sin, and how do I plot a parametrized graph (f(r),g(r))?

Answer 1

To evaluate the integrals at each value in r,

x = arrayfun(f,r);