Find the area enclosed by `y=g(x),` x-axis, x=1 and x=37, where g(x) is inverse of `f(x)=x^(3)+3x+1`.

Explanation

To find the area enclosed by the curve \( y = g(x) \), the x-axis, and the vertical lines \( x = 1 \) and \( x = 37 \), where \( g(x) \) is the inverse of \( f(x) = x^3 + 3x + 1 \), we can follow these steps:

### Step 1: Set up the integral for the area
The area \( A \) can be expressed as:
\[ A = \int_{1}^{37} g(x) \, dx \]
Since \( g(x) \) is the inverse of \( f(x) \), we can rewrite this as:
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