Question

Let $I=\underset{10}{\overset{19}{\int }}\frac{\sin x}{1+x^8}dx.$Then

• A. $|I|<{10}^{-9}$
• B. $|I|<{10}^{-7}$
• C. $|I|<{10}^{-5}$
• D. $|I|>{10}^{-7}$

Answer 1

The correct option is D $|I|>{10}^{-7}$

$I=\underset{10}{\overset{19}{\int }}\frac{\sin x}{1+x^8}dx\because \sin x\le 1\therefore \underset{10}{\overset{19}{\int }}\frac{\sin x}{1+x^8}dx\le \underset{10}{\overset{19}{\int }}\frac{1}{1+x^8}dxI\le$