Improper integrals

The improer integral

 $\int_0^{\infty}e^{-2x}dx$  

• has value 1

• has value 1/2

• has value -1/2

• does not converge

The improper integral

 $\int_0^{\infty}\left(\frac{x}{1+x^2}\right)dx$  

• has value 0

•  has value 1

• does not exist

• has value  1/2

The improper integral

 $\int_0^{\infty}\frac{x}{\left(1+x\right)^2}dx$  

• has value 1

•  has value 0

• has value  2

• does not exist

The integral

 $\int_0^{\frac{\pi}{2}}\frac{\sin\theta}{\sqrt{\cos\theta}}d\theta$  

• does not exist

• has value 1/2

• has value -2

• has value 2

The improper integral

 $\int_1^{\infty}\frac{1}{x\ln x}dx$  

• does not converge

• has value 0

• has value 1

• has value 2e

The improper integral

 $\int_0^{\infty}xe^{-2x}dx$  

• does not exist 

• has value 1

• has value 1/4

• has value 1/2

The improper integral

$\int_0^e\left(\frac{\ln x}{\sqrt{x}}\right)dx$

• has value $-2e^{\frac{1}{2}}$

• has value $-0.25e^{\frac{1}{2}}$

• has value $2e^{\frac{1}{2}}-4e^{-\frac{1}{2}}$

• does not exist