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  • Explain solution RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 20 maths

Explain solution RD Sharma class 12 chapter Areas of Bounded Region exercise 20.1 question 20 maths

Answers (1)

Answer:

3+16\log 2\; s q \cdot { unit }

Hint:

Use the concept of definite integrals.

Given:

Find area of region bounded by curve x y-3 x-2 y-10=0, x-a x i s and line x=3, x=4

Solution:

Given curve,

\begin{aligned} &x y-3 x-2 y-10=0 \\\\ &x y-2 y=3 x+10 \\\\ &y(x-2)=3 x+10 \\\\ &y=\frac{3 x+10}{x-2} \end{aligned}

Area of bounded curve x y-3 x-2 y-10=0, x-a x i s and line x=3, x=4

        \begin{aligned} &\int_{3}^{4}|y| d x=\int_{3}^{4}\left(\frac{3 x+10}{x-2}\right) d x \\\\ &=\int_{3}^{4}\left(\frac{3 x-6+16}{x-2}\right) d x \\\\ &=\int_{3}^{4}\left(3+\frac{16}{x-2}\right) d x \end{aligned}

        \begin{aligned} &=[3 x+16 \log |x-2|]_{3}^{4} \\\\ &=12+16 \log |2|-9-16 \log |1| \\\\ &=16 \log 2+3 \text { sq.unit } \end{aligned}

 

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