The area bounded by the parabola y = x 2 + x + 1 , its tangent at P 1 , 3 , line x = - 1 and the x -axis is A sq units. Then, the value of 6 A is equal to

Step-by-step solution

y = x 2 + x + 1 d y d x = 2 x + 1 At P , d y d x = 3 ∴ tangent is y - 3 = 3 x - 1 or y = 3 x Hence, the area A = ∫ - 1 1 x 2 + x + 1 d x - A r e a of ∆ O P N = x 3 3 + x 2 2 + x − 1 1 − 1 2 ⋅ 3 ⋅ 1 = 2 3 + 2 - 3 2 = 7 6 sq. units ∴ 6 A = 7 i.e. a prime number