estimating definite integral

Question

absolute  value of ∫(sinx)/(1+x⁸) from 10 to 19 is less than

1. 10^-10
2. 10^-11
3. 10^-7
4. 10^-9

Answer 1

|∫(sinx)/(1+x⁸)dx| ≤∫|(sinx)/(1+x⁸)|dx≤∫1/(1+x⁸)dx=

|To estimate, one needs limits of integration. Depending on lower and upper bounds, you can estimate 1/(1+x⁸).  You have to separate intervals, where |x|≤1 and |x|>1|.