# Think More , Calculate Less !

Calculus Level 5

$\left| 3\sin x - 4\cos x + t + \cfrac 4t \right|$

For all real $$t$$, let $$f(t)$$ be the minimum of the above expression over $$x\in \mathbb{R}$$.

Let $$\displaystyle \int_1^{10} f(t) \, dt = 4 ( a + \ln b )$$ for some rational $$a$$ and $$b$$.

Find the value of $$a + 2b$$.

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