Question

Find the area of the region bounded by the lines 2y + x = 8, x = 2 and x = 4.

Answer 1

Given area are 2y + x = 8, x = 2 and x = 4

Required area = `int_2^4 y dx`

                       = `int_2^4 ([ 8 - x ]/2) dx`

                       = `int_2^4 (4 -1/2x)dx`

                       = `[ 4x - 1/2 x^2/2]_2^4`

                      =  `[ 4 xx 4 - 1/4 (4)^2] - [ 4 xx 2 - 1/4 (2)^2 ]`

                      = 12 - 7 = 5
∴ Required area = 5 sq. units