Answer :

Given equations are:

2y = 5x + 7 ...... (1)


x = 2 ...... (2)


x = 8 ...... (3)


Equation (1) represents line passing through and . Equation (2), (3) shows line parallel to y - axis passing through (2,0), (8,0) respectively.


A rough sketch of curves is as below:


12.PNG


We have to find the area of shaded region.


Required area


= (shaded region ABCDA)


(the area can be found by taking a small slice in each region of width Δx, then the area of that sliced part will be yΔx as it is a rectangle and then integrating it to get the area of the whole region)


(As x is between (2,8) and the value of y varies)


(as )




Now integrating by applying power rule, we get



Now applying the limits we get





Hence the area of the region bounded by the line 2y = 5x + 7, x - axis the lines x = 2 and x = 8 is equal to 96 square units.


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