R=(x,y):max(0,logex)≤y≤2x,21≤x≤2
So, the area of the region is
∫2122xdx−∫12ℓnxdx
=[ln22x]1/22−[xlnx−x]12
=loge2(22)−21/2−(2ln2−1)
=loge2(22−2)−2ln2+1
∴α=22−2,β=−2,γ=1
So, (α+β−2γ)2
=(22−2−2−2)2
=(−2)2=2
If the area of the bounded region R=(x,y):max0,logex≤y≤2x,21≤x≤2 is, α(loge2)−1+β(loge2)+γ then the value of (α+β−2γ)2 is equal to:
Held on 27 Jul 2021 · Verified 6 Jul 2026.
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