Answer
$P^{1/2}$ - $\frac{t^{3/2}}{3}$ = $\sqrt 2$ - $\frac{1}{3}$
(OR)
$P^{1/2}$ - $\frac{t^{3/2}}{3}$ = 1.08
Work Step by Step
$\int \frac{dP}{\sqrt P}$ = $\int \sqrt tdt$
$\int P^{-1/2}dP$ = $\int t^{1/2}dt$
$\frac{P^{1/2}}{1/2}$ = $\frac{t^{3/2}}{3/2}$ + c
$2P^{1/2}$ = $\frac{2t^{3/2}}{3}$ + c
$P^{1/2}$ = $\frac{t^{3/2}}{3}$ + c
$P^{1/2}$ - $\frac{t^{3/2}}{3}$ = c ...... (1)
We know that, P(1) = 2, so:
$\sqrt 2$ - $\frac{1}{3}$ = c ......(2)
Using (1) and (2):
$P^{1/2}$ - $\frac{t^{3/2}}{3}$ = $\sqrt 2$ - $\frac{1}{3}$
Hence, $P^{1/2}$ - $\frac{t^{3/2}}{3}$ = 1.08
