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  • please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 2 maths textbook solution

please solve RD sharma class 12 chapter 20 Areas Of Bounded Region exercise Fill in the blanks question 2 maths textbook solution

Answers (1)

\frac{297}{6} sq.units

Hint:

Use indefinite integral formula then put limits to solve this integral

Given:

y=x^{2}+x,x-axis\\ x=2,x=5

Explanation:

Required area,

\begin{aligned} &=\int_{2}^{5}\left(x^{2}+x\right) d x \\ &=\left[\frac{x^{3}}{3}+\frac{x^{2}}{2}\right]_{2}^{5} \\ \end{aligned}

\begin{aligned}&=\left[\frac{(5)^{3}}{3}+\frac{(5)^{2}}{2}\right]-\left[\frac{(2)^{3}}{3}+\frac{(2)^{2}}{2}\right]&&&&&&&& \quad\left[\because \int_{a}^{b} x^{n} d x=\left[\frac{x^{n+1}}{n+1}\right]_{a}\right] \\ \end{aligned}

\begin{aligned} &=\frac{125}{3}-\frac{8}{3}+\frac{25}{2}-\frac{4}{2} \\ &=\frac{117}{3}+\frac{21}{2} \\ \end{aligned}

=\frac{297}{6} sq.units

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