Area bounded by parabola y 2 = x and straight line 2y = x is Options: A . &nbsp43 B . &nbsp1 C . &nbsp23 D . &nbsp13

Answer: Option A : A y 2 = x a n d 2 y = x ⇒ y 2 = 2 y ⇒ y = 0 , 2 ∴ R e q u i r e d a r e a = ∫ 2 0 ( y 2 − 2 y ) d y = ( y 3 3 − y 2 ) 2 0 = 4 3 s q . u n i t

Area bounded by parabola y2=x and straight line 2y = x is

Question

Area bounded by parabola

y^{2} = x

and straight line 2y = x is

Options:

A . 43

B . 1

C . 23

D . 13

Answer: Option A
:
A

y^{2} = x a n d 2 y = x \Rightarrow y^{2} = 2 y \Rightarrow y = 0, 2

∴ R e q u i r e d a r e a = \int_{0}^{2} (y^{2} - 2 y) d y = {(\frac{y^{3}}{3} - y^{2})}_{0}^{2} = \frac{4}{3} s q . u n i t

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