Is multiplying a scalar after the integration of x(t)dt, the same thing as taking the integral of a scalar time x(t)dt?? Will I get the same answer no matter what function is there.

Question

Is multiplying a scalar after the integration of x(t)dt, the same thing as taking the integral of a scalar time x(t)dt??  Will I get the same answer no matter what function is there.

anonymous · Answer

Yes, so long as the scalar is constant with respect to the variable we are integrating over.

anonymous · Answer

If W consists of all functions x(t) in C(1) satisfying the integral x(t)dt=0, can I use w(1) = integral f(t)dt=0 and w(2) = inegral g(t)dt=0, and show it is closed under addition.  Is that how I would label each function set?