Using integration find the area of the triangular region whose sides have the equations

y=2x+1

y=3x+1

x=4

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y = 2x + 1                ..............1

y = 3x + 1                   ..............2

x = 4                   ..........3

line 1 & 2 intersect at P = (0,1)

now , both of these lines are intersected by line 3 so let point of

intersection be Q,R then

P = (4,9)                          (intersection of line 1 with x = 4)

Q = (4,13)                       (intersection of line 2 with x = 4)

now area bw all these lines is area of triangle formed by P,Q,R

A = L₂ - L₂ dx lim from 0 to 4

A = (3x+1)-(2x+1)     lim from 0 to 4

A = xdx      lim from 0 to 4

A = 8 square units