Integration Techniques and Improper Integrals

What makes an integral improper?

• Finite

• Infinite

• Continuous

• Discontinuous

There are ____ cases of L'Hopital's rule.

• 2

• 5

• 7

• 8

Which of the following cases can you use L'hopital's rule?

• 
• 
• 
• 

• Converges

• Diverges

• Converges

• Diverges

• converges

• diverges

• ln 3

• ln 2

• ln (½)

• diverges

The integral above is improper because it is

• finite

• infinite

• continous

• discontinous

• $diverges\ to\ \infty$

• 
  

  $converges\ to\ \frac{\pi}{2}$

• $converges\ to\ \frac{1}{4}$

• $converges\ to\ \frac{\pi}{4}$

• $diverges\ to\ -\infty$

• They are all convergent.

• They are all divergent.

• I is convergent; II and III are divergent.

• II and III are convergent; I is divergent.

• II is convergent; I and III are divergent.