The area of the region bounded by the lines y=2x+1y=3x+1 and x=4 is

Options

A. 16 sq unit
B. `(121)/(3)` sq unit
C. `(121)/(6)` sq. unit
D. `8` sq unit

Answer

D

Explanation

Table for line `y = 2x+ 1`


Area of shaded region `= 1/2|{:(0,1,1),(4,9,1),(4,13,1):}|`
`[ :' "Area of triangle" = 1/2 |{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|]`
`= 1/2[0(9-13)-1(4-4)+1(4xx13-4xx9)]`
`= 1/2[0-0+4(13-9)]=1/2 xx 4 xx 4 = 8` sq units