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  • The area of the region bounded by parabola y2 = x and the straight line 2y = x is A. sq units

The area of the region bounded by parabola y^{2} = x and the straight line 2y = x is
A. \frac{4}{3}  sq units
B. 1 sq units
C. \frac{2}{3}  sq units
D. \frac{1}{3}  sq units

Answers (1)

A)

The questions gives parabola y^2 = x and a straight line 2y = x

 

By substituting for x

\\ $\Rightarrow y^{2}=2 y$\\ $\Rightarrow y(y-2)=0$\\ $\therefore y=0,2$\\ $\therefore x=2 \\y=0,4$\\

Required area

\\ =\int_{0}^{4}\left[\sqrt{\mathrm{x}}-\frac{\mathrm{x}}{2}\right] \mathrm{d} \mathrm{x} \\ =\left[\frac{2 \mathrm{x} \frac{3}{2}}{3}-\frac{\mathrm{x}^{2}}{4}\right]_{0}^{4} \\ =\left(\frac{16}{3}-4-0+0\right) \\ =\frac{4}{3} \mathrm{sq} . \text { units }

 

 

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infoexpert22

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