Let the area of the region enclosed by the curves y=3 x, 2 y=27-3 x and y=3 x-x x be A . Then 10 A is equal to

Step-by-step solution

y=3 x, 2 y=27-3 x & y=3 x-x x aligned & A = ₀^3 3 x -(3 x - x x ) dx + ₃^9 ( 27-3 x 2 -(3 x - x x ) ) dx & A = ₀^3 x ^ 3 / 2 dx + ₃^9 27 2 - 9 x 2 + x ^ 3 / 2 dx & A = [ 2 x ^ 5 / 2 5 ]₀^3+ 27 2 [ x ]₃^9- 9 2 [ x ^2 2 ]₃^9+ [ 2 x ^ 5 / 2 5 ]₃^9 & ~A = 2 5 (3^ 5 / 2 )+ 27 2 (6)- 9 4 (72)+ 2 5 (9^ 5 / 2 -3^ 5 / 2 ) & A = 2 5 (3^ 5 / 2 )+81-162+ 2 5 3^5- 2 5 3^ 5 / 2 & ~A = 486 5 -81= 81 5 & 10 ~A =162 & Ans. =(2) aligned