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Max value of $$\int_{a-1}^{a+1} \frac{1}{1+ x^8} \,dx$$is attained at what value of a?

My attempt:

Let the given integral be $\alpha$ . Then the max value can be calculated by differentiating the term. So for differentiating, i used the Newton-Leibniz rule but all i could infer from the result was that the function $\alpha$ is monotonous. I don't know what else to do. Any inputs will be appreciated.

Arshiya
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1 Answers1

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The function is actually decreasing for $a>0$ and increasing for $a<0$. Hence the maximum is attained at $a=0$.

Kavi Rama Murthy
  • 311,013