Question

The area of the region enclosed by the curve y = x³ and its tangent at the point (-1, -1) is 

(1) 27/4 

(2) 19/4

(3) 23/4 

(4) 31/4

Answer 1

Correct option is (1) 27/4

Equation of tangent : y + 1 = 3 (x + 1) 

i.e. y = 3x + 2 

Point of intersection with curve (2, 8)

So Area = \(\int^{2}_{-1} ((3x+2)-x^3)dx=\frac{27}{4}\)