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The area bounded by the curves  y=2-\left | x-1 \right |\, ,y=sinx;x=0\: and\: x=2 \: \: is;

  • Option 1)

    1+2\cos ^{2}1

  • Option 2)

    2+sin ^{2}1

  • Option 3)

    \frac{\pi}{2}

  • Option 4)

    1+log2

 

Answers (1)

best_answer

As we learnt

Area along x axis -

Let y_{1}= f_{1}(x)\, and \, y_{2}= f_{2}(x) be two curve then area bounded between the curves and the lines

x = a and x = b is

\left | \int_{a}^{b} \Delta y\, dx\right |= \left | \int_{a}^{b}\left ( y_{2}-y_{1} \right ) dx\right |

 

- wherein

Where \Delta y= f_{2}\left ( x \right )-f_{1}(x)

 

  Area=\int_{0}^{1}\left ( 1+x-\sin x \right )dx+\int_{1}^{2}\left ( 3-x-\sin x \right )dx

              =\frac{3}{2}+\left ( \cos 1-1 \right )+3-\frac{3}{2}+\left ( \cos 2 -\cos 1 \right )=2+\cos 2


Option 1)

1+2\cos ^{2}1

Option 2)

2+sin ^{2}1

Option 3)

\frac{\pi}{2}

Option 4)

1+log2

Posted by

Aadil

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