#### To determine

If the given statement is true or false.

#### Answer

False

#### Explanation

Consider fx=x ; a=0, b=1

This function is a polynomial, and so, it is continuous over all real numbers.

Therefore fx is continuous on [0, 1]

Consider,

∫ab[x·f(x)]dx

=∫01x·xdx

=∫01x2 dx

Integrating,

=x3301

Using fundamental theorem of calculus,

= 13-0

= 13

Now consider,

x·∫abfxdx

=x·∫01xdx

Integrating,

=x·x2201

Using fundamental theorem of calculus,

x·12-0

=x2

Since both answers are different, so

∫abx·fxdx≠ x·∫abfxdx

Thus we have produced a counter example to the given statement. So the given statement is in general false.

**Conclusion:**

The given statement is false.