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  • How to solve this problem- Compute the area of the region bounded by the straight lines x = 0, x = 2 and the curves y = 2x, y = 2x – x2.

Compute the area of the region bounded by the straight lines x = 0, x = 2 and the curves y = 2x, y = 2x – x2.

  • Option 1)

    \frac{3}{{\ln 3}} - \frac{4}{3}

  • Option 2)

    \frac{3}{{\ln 2}} - \frac{2}{3}

  • Option 3)

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

  • Option 4)

    none of these

 

Answers (1)

best_answer

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

 

 

Since the maximum of the function
y = 2x - x2 is attained at the point x = 1 and is equal to 1, and the function y = 2x ³ 1 on the interval [0, 2], we have

                        2x > 2x - x2 , for all x Î [0, 2].

                        Hence A = \int\limits_0^2 {\left[ {{2^x} - \left( {2x - {x^2}} \right)} \right]dx}

            =\left ( \frac{2^{x}}{\ln 2} -x^{2}+\frac{x^{3}}{3}\right )_0^{2}

 

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


Option 1)

\frac{3}{{\ln 3}} - \frac{4}{3}

Option 2)

\frac{3}{{\ln 2}} - \frac{2}{3}

Option 3)

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

Option 4)

none of these

Posted by

gaurav

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