The area of the region bounded by the curve 5 | vedclass

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Question

(A) The given curve is $5y = 5 - x$,which can be written as $y = 1 - \frac{x}{5}$.To find the area bounded by the curve,the $X$-axis,and the lines $x

Vedclass · Accepted Answer

$1.5$

Vedclass · Answer

(A) The given curve is $5y = 5 - x$,which can be written as $y = 1 - \frac{x}{5}$.To find the area bounded by the curve,the $X$-axis,and the lines $x = 1$ and $x = 4$,we use the definite integral:$	ext{Area} = \int_{1}^{4} y \, dx$$	ext{Area} = \int_{1}^{4} (1 - \frac{x}{5}) \, dx$Integrating with respect to $x$:$	ext{Area} = [x - \frac{x^2}{10}]_{1}^{4}$Substitute the limits:$	ext{Area} = (4 - \frac{16}{10}) - (1 - \frac{1}{10})$$	ext{Area} = (4 - 1.6) - (1 - 0.1)$$	ext{Area} = 2.4 - 0.9 = 1.5$Thus,the area is $1.5$ sq. units,which is $\frac{3}{2}$ sq. units.

The area of the region bounded by the curve $5y = 5 - x$,the $X$-axis,and the lines $x = 1$ and $x = 4$ is . . . . . . sq. units.

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