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Using integration, find the area of the ...

Using integration, find the area of the region bounded by the line 2y = 5x + 7, the x-axis, and the lines x = 2 and x = 8.

A

96 sq units

B

72 sq units

C

`13(1)/(2)` sq units

D

14 sq units

Text Solution

Verified by Experts

The correct Answer is:
A
`therefore` Required area
`=int_(2)^(8)ydx=int_(2)^(8)(5x+7)/(2)dx`
`=(1)/(2)[(5x^(2))/(2)+7x]_(2)^(8)=(1)/(2)[{(5(64))/(2)+56}-{(5(4))/(2)+14}]`
`=(1)/(2)[(160+56)-(10+14)]=(1)/(2)(216-24)=(192)/(2)`
= 96 sq units
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