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Consider the regions A={(x,y)|x^(2)+y^(2...

Consider the regions `A={(x,y)|x^(2)+y^(2)le100} and B=|(x,y)|sin(x+y)gt0}` in the plane. Then the area of the region `AnnB` is

A

`10pi`

B

100

C

`100pi`

D

`50pi`

Text Solution

Verified by Experts

The correct Answer is:
D
`x^(2)+y^(2)le100`
`rArr "Points lies inside circle or on the circle."`
`sin(x+y)gt0`
`x+y in (0,pi)uu(2pi,3pi)..`
`x+y=c` is equation of a line
Required area is shown in the following figure :

`"Required area = shaded region"`
`"= Half of the area of the circle "`
`=(1)/(2)pi(10)^(2)=50pi`
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