Question

The absolute value of ${\int }_{10}^{19}\frac{cosx}{1+x^8}dx$, is

• A. less than ${10}^{-7}$
• B. more than ${10}^{-7}$
• C. less than ${10}^{-8}$
• D. none of these

Answer 1

The correct option is A less than ${10}^{-7}$

For x $\ge$ 10, we have
$|cosx|<1$ and $1+x^8\ge {10}^8\Rightarrow \frac{1}{1+x^8}\le {10}^{-8}$
$\therefore \left|{\int }_{10}^{19}\frac{cosxdx}{1+x^8}\right|\le {\int }_{10}^{19}\frac{|cosx|}{1+x^8}dx\le {\int }_{10}^{19}{10}^{-8}=9\times {10}^{-8}<{10}^{-7}$