Improper integrals Knowledge-Based Practice

Math · Calculus · Math · Calculus BC Topics

5 Math practice questions on Improper integrals. Questions that assess core concepts and understanding.

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Questions

1.
What is the value of the improper integral $\int_{0}^{1} \frac{\ln x}{\sqrt{x}} \, dx$ ?
- A) $-2$
- B) The integral diverges
- C) $-8$
- D) $-4$
2.
What is the value of the improper integral $\int_{2}^{\infty} \frac{1}{x^2 - 1} \, dx$ ?
- A) $\ln 3$
- B) $\frac{1}{2}\ln 3$
- C) $\ln 2$
- D) The integral diverges
3.
What is the value of the improper integral $\int_{1}^{\infty} \frac{\ln x}{x^2} \, dx$ ?
- A) 1
- B) $\frac{1}{2}$
- C) 2
- D) The integral diverges.
4.
What is the value of the improper integral $\int_{2}^{\infty} \frac{1}{x (\ln x)^2} \, dx$ ?
- A) $\frac{1}{2}$
- B) $\ln 2$
- C) $1$
- D) $\frac{1}{\ln 2}$
5.
What is the value of the improper integral $\int_{0}^{\infty} \frac{e^x}{1 + e^{2x}} \, dx$ ?
- A) $\frac{\pi}{2}$
- B) 1
- C) $\frac{\pi}{4}$
- D) The integral diverges

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