Determine whether the integral is convergent or divergent. | Mathematics I 2074

Mathematics I20745 marksNumerical: improper integral convergenceImproper integrals

Determine whether the integral is convergent or divergent. $\int_1^{\infty} \frac{1}{x} dx$ [5]

Determine whether the integral is convergent or divergent. $$\int_1^{\infty} \frac{1}{x} dx$$ [5]

Integral: $\displaystyle \int1^{\infty} \frac{1}{x}\, dx$ - Lower limit: $1$ , Upper limit: $\infty$ - Integrand: $\frac{1}{x}$ Since the upper limit is infinite, this is an improper integral of Type 1: $\int1^{\infty} \frac{1}{x}\, dx = \lim{t \to \infty} \int1^{t} \frac{1}{x}\, dx$ The antid...

Integral: $\displaystyle \int1^{\infty} \frac{1}{x}, dx$ - Lower limit: $1$, Upper limit: $\infty$ - Integrand: $\frac{1}{x}$ Since the upper limit is infinite, this is an improper integral of Type 1: $$\int1^{\infty} \frac{1}{x}, dx = \lim{t \to \infty} \int1^{t} \frac{1}{x}, dx$$ The antid...