state gov RPSC 2nd Grade Senior Teacher Mock Test Series 2025 Mathematical Science Analysis Improper Integrals
For p ∈ \(\mathbb{R}\), consider the improper integral
\(I_p=\int_0^1 t^p \sin t\, d t\)
Which of the following statements are true?
1
lp is convergent for p = -1/2
2
lp is divergent for p = -3/2
3
lp is convergent for p = 4/3
4
lp is divergent for p = -4/3
5
Question Not Attempted