The area (in sq. units) of the region A=\left \{ (x,y)\epsilon R\times R\left |0 \leq x\leq 3,0\leq y\leq 4,y\leq x^{2}+3x \right \} is :
 

  • Option 1)

    \frac{53}{6}

  • Option 2)

    \frac{59}{6}

  • Option 3)

    \frac{26}{3}

     

  • Option 4)

    8

Answers (1)
S solutionqc

A=\left \{ (x,y)\epsilon R\times R\left |0 \leq x\leq 3,0\leq y\leq 4,y\leq x^{2}+3x \right \}

=y=A

Area of OCD         x=1

\int_{0}^{1}(4-x^{2}-3x)d\; x=\; 4x-\frac{x^{3}}{3}-\frac{3x^{2}}{2}\mid _{0}^{1}

                                              =4\times1-\frac{1}{3}-\frac{3}{2}-0

                                               =4-\frac{1}{3}-\frac{3}{2}

                                               =4-\left ( \frac{2+3}{6} \right )

                                                =\frac{24-11}{6}=\frac{13}{6}

Area of DA BD - Area of OCD=3\times4-\frac{13}{6}

                                                =\frac{72-13}{6}=\frac{59}{6}


Option 1)

\frac{53}{6}

Option 2)

\frac{59}{6}

Option 3)

\frac{26}{3}

 

Option 4)

8

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