Question

Find the area bounded by the curve g(x), the x-axis, the ordinates x = – 1 and x = 4, where g (x) is the inverse of the function f(x) = (x³/24) + (x²/8) + (13/12x) + 1. 

Answer 1

The required area will be equal to area enclosed by y = f(x) and the y-axis between the abscissa y = –1 and y = 4  

∴ f(0) = 1, f(–2) = –1, f(2) = 4 

Clearly, f(x) is monotonic in [–2, 2]. 

Hence, the required area

= 16/3 sq.u.