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  • Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 35 Maths.

Explain solution RD Sharma Class 12 Chapter 20 Areas of Bounded Regions exercise 20.3 question 35 Maths.

Answers (1)

Answer:

 1sq.unit.

Hints:

 Use concept.

Given:

The curves y=\left | x-1 \right | and y=1.

Solution:

To find area bounded by y=\left | x-1 \right |  and y=1

y=\left\{\begin{array}{l} x-1, \text { if } x \geq 0 \\ 1-x, \text { if } x<0 \end{array}\right.

A rough sketch of the curve is as under:

Shaded region is the required area. So

Required area = Region ABCA

A = Region ABDA + Region BCDB

\begin{aligned} &=\int_{0}^{1}\left(y_{1}-y_{2}\right) d x+\int_{1}^{2}\left(y_{1}-y_{3}\right) d x \\ &=\int_{0}^{1}(1-1+x) d x+\int_{1}^{2}(1-x+1) d x \\ &=\int_{0}^{1} x d x+\int_{1}^{2}(2-x) d x \\ &=\left(\frac{x^{2}}{2}\right)_{0}^{1}+\left(2 x-\frac{x^{2}}{2}\right)_{1}^{2} \\ &=\left(\frac{1}{2}-0\right)+\left[(4-2)-\left(2-\frac{1}{2}\right)\right] \\ &=\frac{1}{2}+\left(2-2+\frac{1}{2}\right) \end{aligned}

A = 1 sq. units.

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