If A is the area in the first quadrant enclosed by the curve C : 2 x 2 - y + 1 = 0 , the tangent to C at the point 1 , 3 and the line x + y = 1 , then the value of 60 A is................

Step-by-step solution

Given, y = 2 x 2 + 1 Now tangent to above equation at 1 , 3 is given by, y - 3 = 4 x - 1 ⇒ y = 4 x - 1 Now plotting the diagram we get, Required area of bounded region will be, A = ∫ 0 1 2 x 2 + 1 d x - area of   △ Q O T   - area of   △ P Q R   + area of   △ Q R S ⇒ A = 2 3 + 1 - 1 2 - 9 8 + 9 40 = 16 40 ⇒ 60 A = 16