If the area of the region bounded by the curves y=x^2, y=1x and the lines y=0, x=t (t1) i…

Question

If the area of the region bounded by the curves $y=x^2$, $y=\dfrac1x$ and the lines $y=0$, $x=t$ $(t>1)$ is $1$ sq. unit, then $t$ is equal to:

Accepted Answer

The curves $y=x^2$ and $y=1/x$ meet at $(1,1)$.

$$1 = \int_0^1 x^2\,dx + \int_1^t\frac1x\,dx = \frac13 + \ln t$$

$$\ln t = \frac23 \implies t = e^{2/3}$$

Solutions · 1