Application of Integrals — Class 12 Maths Solution

We have, $2y = 5x + 7$
or $y = \frac{{5x}}{2} + \frac{7}{2}$
The graph is as shown in the adjacent figure.

From the figure, area of shaded region

$= \int_2^8 {\frac{{5x + 1}}{2}} dx$

$= \frac{1}{2}\left[ {5 \cdot \frac{{{x^2}}}{2} + 7x} \right]_2^8$

$= \frac{1}{2}[5 \times 32 + 7 \times 8 - 10 - 14]$

$= \frac{1}{2}[160 + 56 - 24] = 96$ sq, units