Improper Integrals

Question

The value of ∫₁^∞ (1/x²) dx is

RankGuru · Accepted Answer

1. **Define Improper Integral**: Treat the upper limit as a limit to infinity.
   - $\lim_{b 	o \infty} \int_1^b x^{-2} dx$.
2. **Integrate**: Antiderivative is $-1/x$.
   - $[-\frac{1}{x}]_1^b = (-\frac{1}{b}) - (-\frac{1}{1})$
   - $= 1 - \frac{1}{b}$.
3. **Take Limit**: As $b 	o \infty, \frac{1}{b} 	o 0$.
   - Result $= 1 - 0 = 1$.
- Because the limit is finite, we say this improper integral converges to 1.

Rank Guru

Improper Integrals

Select the correct option:

Solution

🔒 Solution Hidden from View

About This Question

Solution