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

Mathematics - Area Under Curves Question with Solution | TestHub

MathematicsArea Under CurvesArea bounded by Miscellaneous CurvesHard2 minPYQ_2016

MathematicsHardsingle choice

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

Answer:

Solution:

The given equation is

$A = \{(x, y) | y \geq x^{2} - 5 x + 4, x + y \geq 1, y \leq 0\}$ is

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

Required area $= \frac{1}{2} \times 2 \times 2 + |\int_{3}^{4} (x^{2} - 5 x + 4) d x|$

$= 2 + {[\frac{x^{3}}{3} - \frac{5 x^{2}}{2} + 4 x]}_{3}^{4}$

$= 2 + \frac{7}{6} = \frac{19}{6} s q . u n i t s$

Stream:JEESubject:MathematicsTopic:Area Under CurvesSubtopic:Area bounded by Miscellaneous Curves

⏱ 2mℹ️ Source: PYQ_2016

Loading discussions...