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.

Plot the line 2y = 5x + 7

We need two points to plot the line, we can get those two points by putting x = 0 and then putting y = 0

Put x = 0

⇒ 2y = 5(0) + 7

Put y = 0

⇒ 2(0) = 5x + 7

⇒ 5x = -7

Hence and are the required two points to draw the line 2y = 5x + 7

x = 2 and x = 8 are lines parallel to Y-axis passing through (2, 0) and (8, 0) respectively

Plot lines 2y = 5x + 7, x = 2 and x = 8

We have to find area under 2y = 5x + 7 that is y = 1/2(5x + 7) from 2 to 8

⇒ y = 1/2(5x + 7)

Integrate from 2 to 8

Hence the area bounded by given lines is 96 unit²