Question

If \( (m,n) \) is an integer solution of \( \int_1^\infty \left( 1 + y^2 \right) dy \), then the expression for \( (m, n) \) in terms of \( (m+1, n+1) \) is?

• A. \( 2m - n \)
• B. \( \frac{2}{n} \)
• C. \( m + n \)
• D. \( 2m + n \)

Hint:

When integrating functions involving sums, the result can often be simplified based on known identities.

Answer 1

The Correct Option is D

By analyzing the integral and its relationship with the values of \( m \) and \( n \), we determine that the solution is expressed as \( 2m + n \).