The area bounded by the parabola y^2=4 x and the line 2 x-3 y+4=0 , in square unit, is

Step-by-step solution

Intersecting points are x=1,4 aligned & Required area = ₁^4 [2 x - ( 2 x+4 3 ) ] d x & = . 2 x^ 3 / 2 3 / 2 |₁ ^4- . 2 x^2 3 2 |₁ ^4- . 4 3 x |₁ ^4 aligned aligned & = 4 3 (4^ 3 / 2 -1^ 3 / 2 )- 1 3 (16-1) [ 4 3 (4)- 4 3 ] & = 4 3 (7)-5-4= 28 3 -9= 28-27 3 = 1 3 aligned