Question

2. Find the area of the plane figure defined by the inequalities : x2 + y2 <9; x2 + y2 - 6x S 0; (in the first quadrant). Use polar coordinates.

Answer 1

Answer :-

Polar coordinates are a set of values that quantify the location of a point based on 1) the distance between the point and a fixed origin and 2) the angle between the point and a fixed direction.

Given that find the area of the plane figure defined by the inequalities x²ty ² 29, x² + y ² - 6x = 0 converting Pt to polas coordinates x= reaso, yerino conchider x²+42 29 - 2 x²+y²-6x 20 (>2-3)² + y2 29 0 we have scarcord and y=reino Alubstitute Pin equation ® th

[reoso. 3)² + (rhino) ²29 8² broso Lo 846 caso Now entersecting pornt ein feat quadrant In cartelan la serie To polas (2, 3) - Carbelian coordinates, which are located by - moving across an t-axle and up and down y-axis in a rectangular fashion. the

Now to find area of the shaded region we do integratiom wide O1079 131, je moj maj 1941 office bile zah +98 (1+60320) do = " +960 + 4020 +95 + 3 (0-) 737, 9J3ui we got Area = 29- que