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Magazine Problem 356
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{1}^{\infty} \frac{\ln x}{x} d x $$
Problem 357
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{1} \frac{\ln x}{\sqrt{x}} d x $$
Problem 358
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{1} \ln x d x $$
Problem 359
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{-\infty}^{\infty} \frac{1}{x^{2}+1} d x $$
Problem 360
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{1}^{5} \frac{d x}{\sqrt{x-1}} $$
Problem 361
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{-2}^{2} \frac{d x}{(1+x)^{2}} $$
Problem 362
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{\infty} e^{-x} d x $$
Problem 363
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{\infty} \sin x d x $$
Problem 364
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{-\infty}^{\infty} \frac{e^{x}}{1+e^{2 x}} d x $$
Problem 365
Determine whether the improper integrals converge or diverge. If possible, determine the value of the integrals that converge. $$ \int_{0}^{1} \frac{d x}{\sqrt[3]{x}} $$
