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Find the area of the region bouonded by ...

Find the area of the region bouonded by `y^2=4x, x=1, x=4` and x-axis in the first quadrant.

A

`16 - 4sqrt2`

B

`15 - 4sqrt5`

C

`17 - 4sqrt3`

D

`18 - 4sqrt7`

Text Solution

Verified by Experts

Please refer to video for diagram. As per the diagram,
Required area will be,
`Area= int_2^4ydx`
Here, we are given, `y^2 = 9x`
So, we can put `y = 3sqrt(x) `
`Area=3 int_2^4sqrt(x)dx`
`=3(|x^(3/2)/(3/2)|_2^4)`
`Area=3**2/3(8-2sqrt2) = 16 - 4sqrt2`
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