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  4. The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y - 2 :

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Q. The area (in sq. units) of the region bounded by the curve $x^2 = 4y$ and the straight line $x = 4y - 2$ :

JEE MainJEE Main 2019Application of Integrals

Solution:

$x = 4y - 2 \; \& \; x^2 = 4y$
$\Rightarrow \; x^2 = x + 2 \; \Rightarrow \; x^2 - x - 2 = 0$
$x = 2, - 1$
So, $\int^{2}_{-1} (\frac{x +2}{4} - \frac{x^2}{4} ) dx = \frac{9}{8}$