#### To determine

The largest value from ∫12x dx, ∫121xdx, ∫12x dx

#### Answer

**∫12xdx**

#### Explanation

**1) Concept:**

Comparison Property of integral:

If fx≥gx for a≤x≤b, then ∫abfxdx≥ ∫abgxdx

2) **Calculation:**

For 1<x≤2, the relation between 1x, x and x is as follows:

1x<x<x

As thesquare root function is an increasing function on its domain, so

1x<x<x

Now using the comparison property of integral,

∫121xdx <∫12x dx<∫12x dx

So,

∫12x dx has the largest value.

**Conclusion:**

∫12x dx has the largest value.