Question

Using integration, find the area of the region bounded by the line 2y + x = 8 , X−axis and the lines x = 2 and x = 4

Answer 1

Let A be the required area.

Consider the equation 2y + x = 8.

∴ y = `1/2(8 - x)`

∴ Required area = `int_2^4 y  "d"x`

= `int_2^4 1/2(8 - x) "d"x`

= `1/2[8x - x^2/2]_2^4`

= `1/2[(8(4) - 4^2/2) - (8(2) - ^2/2)]`

= `1/2[(32 - 8) - (16 - 2)]`

= 5 sq.units