Improper integrals Knowledge-Based Download PDF

Questions

1. 1.

   What is the value of the improper integral $\int_{1}^{\infty} \frac{1}{x^2 + x} \, dx$?

   • A) 1
   • B) $\ln 2$
   • C) $\ln 4$
   • D) The integral diverges.
2. 2.

   What is the value of the improper integral $\int_{0}^{3} \frac{1}{\sqrt{9 - x^2}} \, dx$?

   • A) $\frac{\pi}{6}$
   • B) $\frac{\pi}{3}$
   • C) $\frac{\pi}{2}$
   • D) It diverges
3. 3.

   What is the value of the improper integral $\int_{0}^{1} \ln x \, dx$?

   • A) 1
   • B) $-1$
   • C) 0
   • D) The integral diverges.
4. 4.

   What is the value of the improper integral $\int_{2}^{\infty} \frac{1}{x (\ln x)^2} \, dx$?

   • A) $\ln 2$
   • B) $\frac{1}{2\ln 2}$
   • C) The integral diverges
   • D) $\frac{1}{\ln 2}$
5. 5.

   What is the value of the improper integral $\int_{0}^{\infty} x e^{-2x} \, dx$?

   • A) $\frac{1}{2}$
   • B) $\frac{1}{4}$
   • C) 1
   • D) The integral diverges.