No computational aids required!

Calculus Level 5

Let f:[0,1]Rf : [0,1] \to \mathbb{R} be a function defined as follows: f(x)=10xsinx+cosx\large f(x) = 10 x^{\sin x + \cos x}

Enter the value of the following expression:

01f(x)dx \left \lfloor \int_0^1 f(x) \, dx\right \rfloor

Details and Assumptions:

  • \lfloor \cdot \rfloor denotes the floor function.
  • This question is meant to be done without computational aids.

Source: CMI enterance examination.
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