Draw a rough sketch to indicate the region bounded between the curve `y^2=4a x` and the line `x=3.` also, find the area of this region.

Explanation

`y^{2}=4 x` represents a parabola with vertex at `(0,0)` and axis of symmetry along the `+` ve direction of `x` axis

`x=3` is a line parallel to `y` axis and cutting `x` axis at `(3,0)`

Since `y^{2}=4 x` is symmetrical about `x` axis ,

`therefore` Required area `{A}={OA} {} {CO}=2 times` area `{OABO}`

Slicing the area above `x` axis into vertical strips of length `=|y|` and width `=d x`

Area of corresponding rectangle `=|y| d x`

The corresponding rectangle moves from `x=0` to `x=3`

`y^{2}=4 x` represents a parabola with vertex at `(0,0)` and axis of symmetry along the `+` ve direction of `x` axis

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