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  • Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 9 maths textbook solution

Answers (1)

Answer:

\frac{4}{3}sq\cdot unit

Hint:

\text { Area of } A B C A=2 \times \text { Area of } A B D A

Given:

Draw the rough sketch of v^{2}+1=x, x \leq 2 .Find area enclosed by curve and line  x=2

Solution:

  

\begin{aligned} &y^{2}+1=x, x \leq 2\\\\ &y^{2}+1=x \Rightarrow y=\sqrt{x-1}\\\\ &\text { Area of } A B C A=2 \times \text { Area of } A B D A\\\\ &A=2 \int_{1}^{2}|y| d x \end{aligned}

\begin{aligned} &A=2 \int_{1}^{2} y d x \quad[y>0 \Rightarrow|y|=y] \\\\ &A=2 \int_{1}^{2} \sqrt{x-1} d x \end{aligned}

\begin{aligned} &A=2\left[\frac{(x-1)^{\frac{3}{2}}}{\frac{3}{2}}\right]_{1}^{2} \\\\ &A=\frac{4}{3}\left[1^{\frac{3}{2}}-0\right] \\\\ &A=\frac{4}{3} s q \cdot \text { unit } \end{aligned}    

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