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  • Provide solution for RD Sharma maths class 12 chapter Areas of Bounded Region exercise 20.1 question 6

Provide solution for RD Sharma maths class 12 chapter Areas of Bounded Region exercise 20.1 question 6

Answers (1)

Answer:

\frac{16}{3}sq\cdot units

Hint:

y=4-x^{2}, x=0, x=2

Given:

Make rough sketch of graph of function y=4-x^{2} ,0\leq x\leq 2 and determine the area enclosed by curve and x-axis ,line x=0 and x=2 .

Solution:

y=4-x^{2} , 0\leq x\leq 2 represent half parabola with vertex \left ( 2,0 \right )

x=2  represent a line parallel to y-axis and cutting axis at \left ( 2,0 \right )

Area required = y dx

\begin{aligned} &A=\text { Area of } O A B O \\\\ &A=\int_{0}^{2}|y| d x \\\\ &A=\int_{0}^{2} y d x \end{aligned}

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

\begin{aligned} &A=8-\frac{8}{3} \\\\ &A=\frac{16}{3} s q \cdot u n i t \quad\left[\because \int_{a}^{b} x^{n} d x=\left[\frac{x^{n+1}}{n+1}\right]_{a}^{b}\right] \end{aligned}

       

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