The area enclosed between the parabolas y^2 = 4x and x^2 = 4y is - Vidyadip

MCQ

The area enclosed between the parabolas ${y^2} = 4x$ and ${x^2} = 4y$ is

A
$\frac{{14}}{3}$ sq. unit
B
$\frac{3}{4}$ sq. unit
C
$\frac{3}{{16}}$ sq. unit
✓
$\frac{{16}}{3}$ sq. unit

✓

Answer

Correct option: D.

$\frac{{16}}{3}$ sq. unit

d
(d) Equations of curves ${y^2} = 4x$ and ${x^2} = 4y.$

The given equations may be written as

$y = 2\sqrt x $ and $y = \frac{{{x^2}}}{4}.$

We know that area enclosed by the parabolas

$ = \int_{\,0}^{\,4} {2\sqrt x \,dx - } \int_{\,0}^{\,4} {\frac{{{x^2}}}{4}dx = \frac{{32}}{3} - \frac{{16}}{3} = \frac{{16}}{3}} \,\, sq. \,unit$.

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