Question

Find the area bounded by the lines y = 5x – 10, X-axis and x = 5.

Answer 1

y = 5x – 10

∴ 5x – y = 10

∴ `x/2 + y/-10` = 1

The line intersect X-axis at (2, 0) and Y-axis at (0, –10)

Required area = `int_2^5y  dx`

= `int_2^5(5x - 10)dx`

= `5int_2^5(x - 2)dx`

= `5[(x - 2)^2/2]_2^5`

= `5/2[9]`

= `45/2`

= 22.5 sq. units