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Find the area of the region bounded by ...

Find the area of the region bounded by the curve `y^2=4x`and the line `x = 3`.

Text Solution

Verified by Experts

`y^(2)=4x` is the equation of a parabola and its graph is symmetric about X-axis.

Now, required area = area of `triangle `OABO
`= 2xx` area of OACO
`=2int_(0)^(3)ydx=2int_(0)^(3)2sqrt(x)dx`
`=4*(2)/(3)[x^(3//2)]_(0)^(3)`
`=(8)/(3)xx3sqrt(3)=8sqrt(3)` sq. units.
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