The area of the region enclosed by the parabola ( y - 2 ) 2 = x - 1 , the line x - 2 y + 4 = 0 and the positive coordinate axes is __________.

Step-by-step solution

Given, ( y - 2 ) 2 = x - 1 and x - 2 y + 4 = 0 Now, plotting the graph of the above equation, we get, Now, from above diagram we get, Required area = ∫ 0 3 x d y - Area of Δ A B C . = ∫ 0 3 ( y - 2 ) 2 + 1 d y - 1 2 × 1 × 2 = ∫ 0 3 y 2 - 4 y + 5 d y - 1 = y 3 3 - 2 y 2 + 5 y 0 3 - 1 = 9 - 18 + 15 - 1 = 5