Area Ques 44
Question
- Find the area of the region bounded by the curves
$ y=x^{2}, y=\left|2-x^{2}\right| \text { and } y=2 \text {, } $
which lies to the right of the line $x=1$.
$(2002,5$ M)
Show Answer
Answer:
Correct Answer: 44.$(\frac{20-12 \sqrt{2}}{3}) \text { sq units }$
Solution:
Formula:
- The points in the graph are
$\therefore$ Required area
$ \begin{aligned} & =\int _{1}^{\sqrt{2}}\left\{x^{2}-\left(2-x^{2}\right)\right\} d x+\int _{\sqrt{2}}^{2}\left\{2-\left(x^{2}-2\right)\right\} d x \\ & =\int _{1}^{\sqrt{2}}\left(2 x^{2}-2\right) d x+\int _{\sqrt{2}}^{2}\left(4-x^{2}\right) d x \\ & =[\frac{2 x^{3}}{3}-2 x]^{\sqrt{2}} +[4 x-\frac{x^{3}}{3}]^{2} \\ & =[\frac{4 \sqrt{2}}{3}-2 \sqrt{2}-\frac{2}{3}+2]+[8-\frac{8}{3}-4 \sqrt{2}+\frac{2 \sqrt{2}}{3}] \\ & =(\frac{20-12 \sqrt{2}}{3}) \text { sq units } \end{aligned} $
BETA
