The Cardinal Sine Evaluation

Calculus Level 4

\[ \large \displaystyle \int_{\pi /6}^{\pi /2} f(x) \, dx + \int_{3/ \pi}^{2/ \pi } g(x) \, dx \]

In mathematics the cardinal sine function or \(\text{sinc}(x) \) is defined as \(f(x) = \frac {\sin(x)}x \). Let \(g(x) \) denote the inverse function of \(f(x) \).

What is the value of the expression given above?


This is an original problem.
Also try The Cardinal Sine Evaluation - Part 2..
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