Find the area bounded by `x=at^2 and y=2 at` between the ordinates corresponding to `t=1 and t=2.`

Explanation

When `t=1, x=a`


When `t=2, x=4 a`


`therefore` Required area `=` Area of the shaded region


`=2 times` Area of the region ABCFA


`=2 int_{a}^{4 a} y_{text {parabola }} d x`


When `{t}=1, {x}={a}`


When `{t}=2, {x}=4 {a}`


` therefore text { Required area }=text { Area of the shaded region } =2 times text { Area of the region ABCFA } =2 int_{a}^{4 a} y_{text {parabola }} quad d x =2 int_{a}^{4 a} sqrt{4 a x} d x `


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