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Question Number 191199 by 073 last updated on 20/Apr/23

Commented by 073 last updated on 20/Apr/23

sheed area=??

$$\mathrm{sheed}\:\mathrm{area}=?? \\ $$

Answered by cortano12 last updated on 20/Apr/23

(1)x^2 =(1/x)⇒x=1 (2) Area =∫_0 ^1 x^2 dx+∫_1 ^2 (1/x) dx+∫_(1/2) ^1 (2−(1/x))dx+∫_1 ^(√2) (2−x^2 )dx Area=(1/3)+ln 2+(2.1−0)−(2.(1/2)+ln 2)+2((√2)−1)−(1/3)(2(√2)−1) Area=(1/3)+2−1+2(√2)−2−((2(√2))/3)+(1/3) Area = ((4(√2)−1)/3)

$$\:\left(\mathrm{1}\right)\mathrm{x}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{x}}\Rightarrow\mathrm{x}=\mathrm{1} \\ $$$$\:\left(\mathrm{2}\right)\:\mathrm{Area}\:=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}+\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{dx}+\underset{\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{2}−\frac{\mathrm{1}}{\mathrm{x}}\right)\mathrm{dx}+\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{2}}} {\int}}\left(\mathrm{2}−\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx} \\ $$$$\:\:\:\mathrm{Area}=\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{ln}\:\mathrm{2}+\left(\mathrm{2}.\mathrm{1}−\mathrm{0}\right)−\left(\mathrm{2}.\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{ln}\:\mathrm{2}\right)+\mathrm{2}\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)−\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{1}\right) \\ $$$$\:\:\:\mathrm{Area}=\frac{\mathrm{1}}{\mathrm{3}}+\mathrm{2}−\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{2}−\frac{\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:\mathrm{Area}\:=\:\frac{\mathrm{4}\sqrt{\mathrm{2}}−\mathrm{1}}{\mathrm{3}} \\ $$

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