Question

$|{\int }_{10}^{19}\frac{sinxdx}{1+x^8}|islessthen$

• A. ${10}^{-10}$
• B. ${10}^{-11}$
• C. ${10}^{-7}$
• D. ${10}^{-9}$

Answer 1

The correct option is B ${10}^{-11}$

$|{\int }_{10}^{19}\frac{sinxdx}{1+x^8}|\le {\int }_{10}^{19}|\frac{sinx}{1+x^8}|dx$
$\le {\int }_{10}^{19}\frac{1}{1+x^8}dx<{\int }_{10}^{19}\frac{dx}{x^8}$
$=\frac{-1}{7}[x^{-7}{]}_{10}^{19}$
=$\frac{1}{7}{10}^{-7}-\frac{1}{7}{19}^{-7}<\frac{1}{7}{10}^{-7}<{10}^{-7}$