Find the area between the line: y= 4x + 2 and x = 2 and x = 3

To find the area between y= 4x+2 and the ordinates at x=2 and x=
3.

We know that y=4x+2 at x= 2  has the y value y = 4*2+2 =
10.

Similarly for x=3, the y value of y= 4x+2 is y = 4*3+2 =
14.

Therefore the area under y= 4x+2  and x axis and the ordinates
at x=2 and x= 3 is the same as the trapezium (2, 10), (2,0) , (3,0) and
(3,14).

So the parallel sides (2,0) To (2,10) and (3,0) to(3,14) are
10 and 14 and the distance between the parallel sides = (3-2) =
1.

Therefore area of the trapezium = (1/2)(sum of the ||
sides)(distance between the parallel sides) = (1/2)(10+14)*1 = 12.