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Area of the region {(x,y)inR^(2): y ge ...

Area of the region `{(x,y)inR^(2): y ge sqrt(|x+3|), 5ylex+9le15}` is equal to

A

`(1)/(6)`

B

`(4)/(3)`

C

`(3)/(2)`

D

`(5)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`ygesqrt|x+3|`
`y^(2)ge{{:(x+3, if x ge -3),(-x-3, if x lt -3):}`

`A=(A("trapezium PQTU"-overset(-3)underset(-4)intsqrt(-x-3)dx)+(A("trapezium QRST")-overset(1)underset(-3)intsqrt(x+3)dx)`
`=((11)/(10)-(2)/(3))+(16)/(15)=(3)/(2)`
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