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Find the area bounded by the curves y = x2, y = [x+1], x\leq 1and the y – axis, where [.] denotes the greatest integer not exceeding x.

  • Option 1)

    2/3

  • Option 2)

    1/3

  • Option 3)

    1

  • Option 4)

    2

 

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)

 

 2 

Area\; Required=1-\int_{0}^{1}ydx=1-\int_{0}^{1}x^{2}dx=\frac{2}{3}


Option 1)

2/3

Option 2)

1/3

Option 3)

1

Option 4)

2

Posted by

prateek

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