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  • Confused! kindly explain, The area (in sq. units) of the region described by A = {(x, y)|y ≥ x2 − 5x + 4, x + y ≥ 1, y ≤ 0} is :

The area (in sq. units) of the region described by A = {(x, y)|y  ≥  x2 − 5x + 4, x + y  ≥  1, y ≤ 0} is :

  • Option 1)  (7/2)
  • Option 2)(19/6)
  • Option 3)(13/6)
  • Option 4) (17/6)
 

Answers (1)

As learnt in concept

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)

 

 Point of intersection of 

y= x2-5x+4 and x+y=1 are x=1,3

at x=1, y=0;

x=3, y= -2

Req Area = Area\: \Delta ABC+\left | \int_{3}^{4}\left ( x^{2}-5x+4 \right )dx \right |

= \frac{1}{2 }\times 2\times 2+\left [ \frac{x^{3}}{3}-\frac{5x^{2}}{2}+4x \right ]^{4}_{3}

=\frac{19}{6}


Option 1)

\frac{7}{2}

Incorrect option    

Option 2)

\frac{19}{6}

Correct option

Option 3)

\frac{13}{6}

Incorrect option    

Option 4)

\frac{17}{6}

Incorrect option    

Posted by

Vakul

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