Given,
![\[2y~=\text{ }5x~+\text{ }7,~x-axis,~x~=\text{ }2\text{ }and~x~=\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-36edd7ca9f8ef35f114f3e9c1dbe2679_l3.png "Rendered by QuickLaTeX.com")
graphg for:
![\[2y~=\text{ }5x~+\text{ }7\text{ }\Rightarrow \text{ }y\text{ }=\text{ }\left( 5x\text{ }+\text{ }7 \right)/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c322bc7475f1923d7c681d5d4dd539df_l3.png "Rendered by QuickLaTeX.com")
is
| x | 1 | -1 |
| y | 6 | 1 |
The area of the required region is
Therefore, the required area the region = 96 sq. units
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x-axis and the lines x = 2 and x = 8.
Using integration, find the area of the region bounded by the line 2y = 5x + 7, x-axis and the lines x = 2 and x = 8.