Question 1
Evaluate the improper integral
![](data:image/png;base64, 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)
![](data:image/png;base64, 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)
dx or show it diverges ( to ∞ or -∞).
◦ diverges to ∞
◦ diverges to -∞
◦ converges to sin(3) - 3cos(3)
◦ converges to 3 - sin(3)
◦ converges to - sin(3)
Question 2
Evaluate, if convergent,
![](data:image/png;base64, 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)
e
-x dx.
◦ 1
◦ -1
◦ 2
◦ -2
◦ diverges to ∞