To determine

To evaluate:

∫19u-2u2udu if it exists

Answer

-76

Explanation

1) Concept:

By using fundamental theorem of calculus and rules of integration evaluate the given integral.

2) Theorem:

Fundamental theorem of calculus:

If f is continuous on [a, b], then ∫abfxdx=Fb-F(a).

3) Formula:

∫xndx=xn+1n+1+C

3) Given:

∫19u-2u2udu

4) Calculation:

Consider, ∫19u-2u2udu

Simplify,

=∫19u12u-2u2udu

=∫19(u-12-2u) du

Since the function is continuous in the given interval, the integral exists.

By applying fundamental theorem of calculus and power rule,

=u1212-2u2219

=(9)1212-(9)2-(1)1212-(1)2

Simplify,

=6-81-(2-1)

=-75-1

=-76

Conclusion:

Therefore, ∫19u-2u2udu=-76