The area enclosed between y2 = 4x, x = 1, x = 4 in the first quadrant is:

Question

The area enclosed between $y^{2} = 4 x,$ $x = 1,$ $x = 4$ in the first quadrant is:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{28}{3}$ sq. unit

Explanation :

We have,

$y^{2} = 4 x$

$y = 2 \sqrt{x}$

So, the area enclosed is given by

$Area = \int_{1}^{4} y d x$

$= \int_{1}^{4} 2 \sqrt{x} d x$

$= 2 \int_{1}^{4} x^{1 / 2} d x$

$= 2 {[\frac{2 x^{3 / 2}}{3}]}_{1}^{4}$

$= \frac{4}{3} [4^{3 / 2} - 1]$

$= \frac{4}{3} [8 - 1]$

$= \frac{4}{3} \times 7 = \frac{28}{3} sq. units$

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