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  • Need solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 30 sub question 1.

Need solution for RD Sharma Maths Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 30 sub question 1.

Answers (1)

Answer:

 11 sq.units.

Hint:

Use concept of definite integrals.

Given:

The given equations are 3x - y -3 =0 , 2x + y - 1 =0 and x -2y -1 =0.

Solution:

We have

\begin{aligned} &3 x-y-3=0 \\ &2 x+y-1=0 \\ &x-2 y-1=0 \end{aligned}

Area of bounded region =

\begin{aligned} &=\int_{0}^{3} 3 x-3-\left(\frac{x-1}{2}\right) d x+\int_{3}^{5} 12-2 x-\left(\frac{x-1}{2}\right) d x \\ &=\left[\frac{3 x^{2}}{2}-3 x-\frac{x^{2}}{4}+\frac{1}{2} x\right]_{0}^{3}+\left[12 x-2 \frac{x^{2}}{2}-\frac{x^{2}}{4}+\frac{1}{2} x\right]_{3}^{5} \\ &=\left[\frac{27}{2}-9-\frac{9}{4}+\frac{3}{2}\right] \\ &=\left[60-25-\frac{25}{4}+\frac{5}{2}-36+9+\frac{9}{4}-\frac{3}{2}\right] \\ &=11 \text { sq.units } \end{aligned}

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