Find the area of the shaded region. f(x) = 8x + 2x -x, g(x) = 0\fSolution : = > Given curves are f ( x) = 8x + 22(2_213 9 (20) = 0 The intersection of these two curves is given by = 821 + 272-213=0. [By BAD] = > 23 - 2202- 821 =0 2 ( x - 2 2 - 8) = 0 - 2 8292- 421+221-83=0 - 2 8 2 ( 2- 4) + 2 ( 21- 9) 3 = 0 2 8 ( 2 + 2) ( 71 - 4 ) = 0 se ( 21 + 2 ) ( 21 - 4 ) = 0 = ) 21 = 0 , - 2, 4 we know that, the area of the region bounded by any two curves fins & I( = 0 gin ) is given by 2 3 X Area = S. If( w - gin ) in Here the limit of integration are the intersections of these two curves So , the area of the given region is = = So - (8+22 2 23] an + S./(82 + 272x3)-07 an By Of = S (23- 2x2 - 8x)d + So(-213+2x"+8ngan = [q x- 3 x3- 4x2 ] 2 + [- 429+ 3 28+ 4x273(09 - (- 2) 4) - 3103- (-2)3) - 4(02 (-2)2) - 4(39-09 ) + 2 ( 3 2 03 ) + 4 ( 32 02 ) - 4 - 16 3 +16 - 81 + 18+ 36 6 6 -. 16 81- 3 732 -64- 243 485 12 1.2 Therefore , the area of the Shaded region is 485 sq. units 12