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#### Pranav

##### Well-known member

- Nov 4, 2013

- 428

**Problem:**

If f is continuous and differentiable function in $x \in (0,1)$ suuch that $\sum_{r=0}^{1}\left(f(x+r)-\left|e^x-r-1\right|\right)$=0, then $\int_0^{11} f(x)\,dx$ is

A)65+4ln2-7e

B)63+4ln2-9e

C)69-9e

D)29-23e

Ans: A

**Attempt:**

I could only write the following:

$$f(x)+f(x+1)+\cdots+f(x+11)=|e^x-1|+|e^x-2|+\cdots+|e^x-11|$$

Since I had no idea how to proceed further, I assumed $f(x)=|e^x-11|$ but evaluating the definite integral with this f(x) doesn't give the right answer.

Any help is appreciated. Thanks!