1.

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

Answer»

`10pi`
100
`100pi`
`50pi`

Solution :`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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