#### To determine

**To evaluate:**

∫1912xdx

#### Answer

∫1912xdx=ln3

#### Explanation

**1) Concept:**

The Fundamental Theorem of Calculus: Suppose f is continuous on [a, b], then

∫abfxdx=Fb-F(a), where F is antiderivative of f, that is F'=f.

**2) Formulae:**

i) anti derivative of 1x=ln x+C

ii) alnb=lnba

**3) Calculations:**

Consider,

∫1912xdx

By taking 12 outside the integral

∫1912xdx=12∫191xdx

By applying formula (i) and using the Fundamental Theorem of Calculus

12∫191xdx=12lnx91=12ln9-ln1

By simplifying the above equation

12[ln9-ln1]=12(ln9)

Using formula (ii),

*12(ln9)=ln912=ln9 =ln3*

**Conclusion:**

Therefore,

∫1912xdx=ln3