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  • Help me answer: - The area (in sq. units) of the region bounded by the parabola,and the lines, is : - Integral Calculus - JEE Main

The area (in sq. units) of the region bounded by the parabola, y=x^{2}+2 and the lines, y=x+1,x=0\: \: and\: \: x=3, is :  

  • Option 1)

    \frac{17}{4}

     

     

     

  • Option 2)

    \frac{15}{2}

  • Option 3)

    \frac{21}{2}

  • Option 4)

    \frac{15}{4}

Answers (1)

best_answer

 

Area between two curves -

\\*I\! \! f \: f\left ( x \right )\geqslant g\left ( x \right )\\* in[a,c)\: \: and \: \: g\left ( x \right ) \geqslant f\left ( x \right )\:in(c,b]\\* Then\: area = \\*\\* \int_{a}^{c}\left ( f\left ( x \right )-g\left ( x \right ) \right )dx+\int_{c}^{b}\left ( g\left ( x \right )-f\left ( x \right ) \right )dx

- wherein

Area = \int_{0}^{3}[(x^{2}+2)-(x+1)]dx

         = \int_{0}^{3}(x^{2}-x+1)dx

        = \frac{15}{2}

 


Option 1)

\frac{17}{4}

 

 

 

Option 2)

\frac{15}{2}

Option 3)

\frac{21}{2}

Option 4)

\frac{15}{4}

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