The area of the region bounded by the line 2y + x = 8, X-axis and the lines x = 2 and x = 4 is:

Question

The area of the region bounded by the line $2 y + x = 8$ , $X$ -axis and the lines $x = 2$ and $x = 4$ is:

Smart Achievers · Accepted Answer

(1)

Ans. 5 sq. units

Explanation:

Required area = Area of the shaded region

$x = 2$

$= \int_{2}^{4} \frac{1}{2} (8 - x) d x$

$= \frac{1}{2} {[8 x - \frac{x^{2}}{2}]}_{2}^{4}$

$= \frac{1}{2} [(8 \cdot (4) - \frac{4^{2}}{2}) - (8 \cdot (2) - \frac{2^{2}}{2})]$

$= 5 sq. unit.$

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