Question

Using integration, find the area of the region bounded by the line y = 5x + 2, the x−axis and the ordinates x = −2 and x = 2.

Answer 1

y = 5x + 2, x = −2, x = 2,

X-аxis plotting 

x	0	`-2/5`
y	2	0

x = 2 line parallel to Y-axis at x = 2

x = −2 line parallel to Y-axis at x = −2

Required Area = `int_(-2)^(-2/5) y  dx + int_(-2/5)^(2) y  dx`

= `int_(-2)^(-2/5) (5x + 2)dx + int_(-2/5)^(2) (5x + 2) dx`

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

= `((5 xx 4)/(2 xx 25) - (2 xx 2)/(5)) - ((5 xx 4)/(2) - 4) + ((5 xx 4)/(2 xx 25) - (2 xx 2)/5)`

= `2/5 - 4/5 - 10 + 4 + 10 + 4 - 2/5 + 4/5`

= 4 + 4

= 8 sq. units