Consider the function $$f(x) = x^3 - 6 x^2 + 42 x + 3$$ By drawing a suitable picture, find a relation between the definite integrals $\displaystyle \int_1 ^2 f(x)\,dx$ and $\displaystyle \int_{40}^{71}f^{-1}(x)\,dx$. Use this relation to find the second of these two integrals

$\displaystyle \int_{40}^{71}f^{-1}(x)\,dx$ =