The area of the regions bounded by the curve y2 = 4x, the X-axis and the lines x = 1, x = 4, y 0, is:

Question

The area of the regions bounded by the curve $y^{2} = 4 x$ , the $X$ -axis and the lines $x = 1$ , $x = 4, y \geq 0$ is:

Smart Achievers · Accepted Answer

(3)

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

Explanation:

$Let A be the required area.$

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

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

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

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

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

$∴$ $A = \frac{28}{3} sq. units.$

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