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7.2 definite integral — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત7.2 definite integral1 Mark
MCQ
$\int_0^1 {\frac{{dx}}{{\sqrt {1 + x} - \sqrt x }} = } $
  • A
    $\frac{{2\sqrt 2 }}{3}$
  • ✓
    $\frac{{4\sqrt 2 }}{3}$
  • C
    $\frac{{8\sqrt 2 }}{3}$
  • D
    એકપણ નહીં.
✓

Answer

Correct option: B.
$\frac{{4\sqrt 2 }}{3}$
b
(b) $I = \int_0^1 {\frac{{dx}}{{\sqrt {1 + x} - \sqrt x }} = \int_0^1 {\frac{{(\sqrt {1 + x} + \sqrt x )dx}}{{(\sqrt {1 + x} - \sqrt x )(\sqrt {1 + x} + \sqrt x )}}} } $

$ = \int_0^1 {\frac{{(\sqrt {1 + x} + \sqrt x )}}{{1 + x - x}}} dx = \int_0^1 {\sqrt {1 + x\,} dx} + \int_0^1 {\sqrt x } dx $

$= \frac{{4\sqrt 2 }}{3}$.

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