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  • Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 12.

Provide solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Region Exercise 20.3 question 12.

Answers (1)

Answer:  

\frac{9}{2}\; \text{sq. units} .

Hint:  Using the formula

Given: The equations of the given curves are

y^2=x            ..........(I)

x+y =2           ........(II)

Solution:   Plot the two curves

y^2=x            ..........(I)

x+y =2           ........(II)

Solving  (I) and (II) ,we have

\begin{aligned} &y^{2}+y=2\\ &(y+2)(y-1)=0\\ &y=-2,1 \end{aligned}

We have to determine the area of shaded region.

Required Area

\begin{aligned} &=\int_{2}^{1}(2-y) d y-\int_{-2}^{1} y^{2} d y \\ &\left.=2 y-\frac{y^{2}}{2}-\frac{y^{3}}{3}\right]_{-2}^{1} \\ &=\left(2-\frac{1}{2}-\frac{1}{3}\right)-\left(-4-\frac{4}{2}+\frac{8}{3}\right) \\ &=\frac{9}{2} \text { square units. } \end{aligned}

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