Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિતસંકલનનો ઉપયોગ1 Mark
MCQ
જો $\int_{0}^{1}\frac{dx}{\sqrt{1+x}-\sqrt{x}}=\frac{k\sqrt{2}}{3},$ હોય,તો $k=\ .......$
A
$6$
B
$7$
C
$8$
✓
$4$
✓
Answer
Correct option: D.
$4$
$1=\int_{0}^{1}\frac{\sqrt{1+x}+\sqrt{x}}{1}dx$
$=\left[\frac{2}{3}((1+x)^{3/2}+x^{3/2})\right]_0^1$
$=\frac{2}{3}[2\sqrt{2}+1-1]=\frac{4\sqrt{2}}{3}.$ ને $\frac{k\sqrt{2}}{3}$ સાથે સરખાવતા,
$\therefore k=4.$
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