If the area of the region bounded by the curves y=x², y=1/x and the lines y=0 and x=t (t>1) is 1 sq. unit, then t is equal to?

Given, y=x², y=1/x
Area bounded by the curves is the region ABCD.
Therefore, area = ∫₁⁰ x²dx + ∫ₜ¹ 1/x dx = [x³/3]₁⁰ + [ln(x)]ₜ¹ = 1/3 + ln(t)
It is given that area enclosed is 1
⇒ 1/3 + ln(t) = 1
⇒ ln(t) = 2/3
⇒ t = e²/³
Hence, answer is option (A)