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

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

JEE MainJEE Main 2016Application of Integrals

Solution:

Required area = $A_1+A_2$
$=\frac{1}{2}\times2\times2+\left|\int^{4}_{3}\left(x^{2}-5x+4\right)dx\right|$
$=2+\frac{7}{6}=\frac{19}{6}$sq units

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