The largest value from ∫12x dx, ∫121xdx, ∫12x dx
Comparison Property of integral:
If fx≥gx for a≤x≤b, then ∫abfxdx≥ ∫abgxdx
For 1<x≤2, the relation between 1x, x and x is as follows:
As thesquare root function is an increasing function on its domain, so
Now using the comparison property of integral,
∫121xdx <∫12x dx<∫12x dx
∫12x dx has the largest value.