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  • please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 1 maths textbook solution

please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 1 maths textbook solution

Answers (1)

\frac{37}{3} Sq. units

Hint:

Use indefinite integral formula then put limits to solve this integral.

Given:

x=y^{2},y-axis

Explanation:

y=3,x=9\;\;\;\;\;\;\;\;\;\;\;\; \left [ \because x=y^{2} \right] \\ y=4,x=16

         

y^{2}=x denotes the curve in the graph.

Area, OABC=\int_{3}^{4}y^{2}dy                                                                                                                                        

         \begin{aligned} &=\left[\frac{y^{3}}{3}\right]_{3}^{4}\\ &=\frac{1}{3}\left[(4)^{3}-(3)^{3}\right] & &&&&&&& \quad\left[\because \int_{a}^{b} x^{n} d x=\left[\frac{x^{n+1}}{n+1}\right]_{a}^{b}\right]\\ &=\frac{1}{3}[64-27]\\ &=\frac{37}{3} \mathrm{sq} \cdot \text { units } \end{aligned}                                          

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