The absolute value of $\int\limits_{10}^{19} \frac{\cos x}{1+x^8} d x$, is
Answer & explanation
Correct answer: option 1
For x > 10, we have
$|\cos x|<1$ and $1+x^8>10^8 \Rightarrow \frac{1}{1+x^8} \leq 10^{-8}$
∴ $\left|\int\limits_{10}^{19} \frac{\cos x d x}{1+x^8}\right| \leq \int\limits_{10}^{19} \frac{|\cos x|}{1+x^8} d x \leq \int\limits_{10}^{19} 10^{-8}=9 \times 10^{-8}<10^{-7}$