Given that

asked 2021-08-12

Evaluate the integrals without using tables.

\(\displaystyle{\int_{{{\frac{{{1}}}{{{2}}}}}}^{{{2}}}}{\frac{{{\left.{d}{x}\right.}}}{{{x}{\ln{{x}}}}}}\)

\(\displaystyle{\int_{{{\frac{{{1}}}{{{2}}}}}}^{{{2}}}}{\frac{{{\left.{d}{x}\right.}}}{{{x}{\ln{{x}}}}}}\)

asked 2021-11-08

Evaluate the integral without using tables.

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{1}-{x}^{{{2}}}}}}}}\)

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\frac{{{\left.{d}{x}\right.}}}{{\sqrt{{{1}-{x}^{{{2}}}}}}}}\)

asked 2021-11-09

Evaluate the integral without using tables.

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\left(-{\ln{{x}}}\right)}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\left(-{\ln{{x}}}\right)}{\left.{d}{x}\right.}\)

asked 2021-11-07

Evaluate the integral without using tables.

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{x}{\ln{{x}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{x}{\ln{{x}}}{\left.{d}{x}\right.}\)

asked 2021-11-10

Evaluate the integral without using tables.

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\frac{{{d}{r}}}{{{r}^{{{0.999}}}}}}\)

\(\displaystyle{\int_{{{0}}}^{{{1}}}}{\frac{{{d}{r}}}{{{r}^{{{0.999}}}}}}\)

asked 2021-08-11

Evaluate the following integrals or stat that they diverge.

\(\displaystyle{\int_{{-\infty}}^{{-{1}}}}{\frac{{{\left.{d}{x}\right.}}}{{{x}^{{{3}}}}}}\)

\(\displaystyle{\int_{{-\infty}}^{{-{1}}}}{\frac{{{\left.{d}{x}\right.}}}{{{x}^{{{3}}}}}}\)

asked 2021-05-29

Evaluate the ff, improper integrals.

\(\int_{1}^{\infty}\frac{1}{x^{3}}dx\)

\(\int_{1}^{\infty}\frac{1}{x^{3}}dx\)