Question

Find the area of the region bounded by the curves x = at² and y = 2at between the ordinate corresponding to t = 1 and t = 2.

Answer 1

Given that x = at²  ......(i)

y = 2at  ......(ii)

t = `y/(2"a")`

Putting the value of t in (i)

Wwe get y² = 4ax

Putting t = 1 and t = 2 in (i)

We get x = a, and x = 4a

Required area = 2 area of ABCD 

= `2 int_"a"^(4"a") y"d"x`

= `2 xx 2 int_"a"^(4"a") sqrt("a"x)  "d"x`

= `8sqrt("a") |(x)^(3/2)/3|_"a"^(4"a")`

= `56/3 "a"^2` sq.units