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  • Need explanation for: Area of the region bounded by the curves y = 2x, y = 2x - x2, x = 0 and x = 2 is given by

Area of the region bounded by the curves y = 2x, y = 2x - x2, x = 0 and x = 2 is given by

  • Option 1)

    \frac{3}{{\log 2}} - \frac{4}{3}

  • Option 2)

    \frac{3}{{\log 2}} + \frac{4}{3}

  • Option 3)

    3\log 2 - \frac{4}{3}

  • Option 4)

    none of these

 

Answers (1)

As we learnt 

 

Area between two curves -

 

If we have two functions f\left ( x \right )\: and\:g \left ( x \right ).Area between two curves are

\int_{a}^{b}\left [ g\left ( x \right )-f\left ( x \right ) \right ]dx

- wherein

 

 Required area

=\int\limits_0^2 {({y_2} - {y_1})\;dx} $

=\int\limits_0^2 {({2^x} - (2x - {x^2}))\;dx}

=\left[ {\frac{{{2^x}}}{{\log 2}} - {x^2} + \frac{{{x^3}}}{3}} \right]_0^2$

=\frac{4}{{\log 2}} - 4 + \frac{8}{3} - \frac{1}{{\log 2}} = \frac{3}{{\log 2}} - \frac{4}{3}$

 


Option 1)

\frac{3}{{\log 2}} - \frac{4}{3}$

Option 2)

\frac{3}{{\log 2}} + \frac{4}{3}$

Option 3)

3\log 2 - \frac{4}{3}$

Option 4)

none of these

Posted by

subam

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