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JEE Main 20169 AprilOnline
Exam
JEE Main
Year
2016
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Area Under Curves

JEE Main 2016 · 9 April · Online · Mathematics · Area Under Curves

The area (in sq. units) of the region described by A = \ (x, y) | y...

The area (in sq. units) of the region described by A={(x,y)∣y≥x2−5x+4,x+y≥1,y≤0}A = \left\{\left(x, y\right) | y \ge {x}^{2} - 5x + 4, x + y \ge 1, y \le 0\right\} isThe area (in sq. units) of the region described by A = \ (x, y) | y ≥ x ^ 2 - 5x + 4, x + y ≥ 1, y ≤ 0\ is

Options

  1. A196\dfrac{19}{6}
  2. B176\dfrac{17}{6}
  3. C72\dfrac{7}{2}
  4. D136\dfrac{13}{6}

Correct answer

A. 196\dfrac{19}{6}

Step-by-step solution

The given equation is

A={(x,y)∣y≥x2−5x+4,x+y≥1,y≤0}A = \left\{\left(x, y\right) | y \ge {x}^{2} - 5x + 4, x + y \ge 1, y \le 0\right\} is

The area (in sq. units) of the region described by A = \ (x, y) | y ≥ x ^ 2 - 5x + 4, x + y ≥ 1, y ≤ 0\ is

The equation x2−5x+4{x}^{2} - 5x + 4 is cutting the x−x - axis at x=1,4x = 1, 4

Required area =12×2×2+∣∫34(x2−5x+4)dx∣= \dfrac{1}{2} \times 2 \times 2 + \left|\mathop{∫}_{3}^{4}\left({x}^{2} - 5x + 4\right)dx\right|

=2+[x33−5x22+4x]34= 2 + {\left[\dfrac{{x}^{3}}{3} - \dfrac{5{x}^{2}}{2} + 4x\right]}_{3}^{4}

=2+76=196sq.units= 2 + \dfrac{7}{6} = \dfrac{19}{6}sq . units

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