#### To determine

If the given statement is true or false.

#### Answer

False

#### Explanation

Consider, fx=x, gx=x2; a=0,b=1

Functions fx=x and gx=x2 are continuous on [0, 1] since these are polynomial functions, and polynomials are continuous over all real numbers.Consider

∫abfxgx dx

= ∫01x·x2dx

= ∫01x3 dx

Integrating,

= x4401

Using fundamental theorem of calculus,

= 14-0

= 14 Now

∫abfxdx·∫abgxdx

=∫01xdx·∫01x2dx

Integrating,

=x2201·x3301

Using fundamental theorem of calculus,

=1 2-0·13-0

By simplifying,

=16

Since both answers are different

∫abfxgx dx ≠ ∫abfxdx·∫abgxdx So we have produced a counter example to the given statement. So it is false.

**Conclusion:**

The given statement is false.