The area of the region bounded by the line 2y | vedclass

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(B) The equation of the line is $2y + x = 8$,which can be written as $y = \frac{8 - x}{2}$.The required area is given by the definite integral $\int_{

Vedclass · Accepted Answer

$5 	ext{ sq. units}$

Vedclass · Answer

(B) The equation of the line is $2y + x = 8$,which can be written as $y = \frac{8 - x}{2}$.The required area is given by the definite integral $\int_{2}^{4} y \, dx = \int_{2}^{4} \frac{8 - x}{2} \, dx$.$= \frac{1}{2} \int_{2}^{4} (8 - x) \, dx$$= \frac{1}{2} \left[ 8x - \frac{x^2}{2} ight]_{2}^{4}$$= \frac{1}{2} \left( (8(4) - \frac{4^2}{2}) - (8(2) - \frac{2^2}{2}) ight)$$= \frac{1}{2} \left( (32 - 8) - (16 - 2) ight)$$= \frac{1}{2} (24 - 14) = \frac{10}{2} = 5 	ext{ sq. units}$.

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

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