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  • The area of the region by  <img alt="\mathrm{\mathrm{A}=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\} }" src="/latex-image/?%5Cmathrm%7B%5Cmathrm%7BA%7D%3D%5Cleft%5C%7B%28x%2C%20

The area of the region by  \mathrm{\mathrm{A}=\left\{(x, y): x^{2} \leq y \leq \min \{x+2,4-3 x\}\right\} }  is :

Option: 1

\frac{31}{8}


Option: 2

\frac{17}{6}


Option: 3

\frac{19}{6}


Option: 4

\frac{27}{8}


Answers (1)

best_answer

\mathrm{A=\int_{-1}^{\frac{1}{2}}\left(x+2-x^{2}\right) d x+\int_{\frac{1}{2}}^{1}\left(4-3 x-x^{2}\right) d x=\frac{17}{6}}

Hence correct option is 2

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mansi

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