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Question

asked 2021-08-13

Evaluate the integrals

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{3}}}}}}}{{\sec}^{{{2}}}{0}}{d}{0}\)

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{3}}}}}}}{{\sec}^{{{2}}}{0}}{d}{0}\)

asked 2021-08-12

Evaluate the following iterated integrals.

\(\displaystyle{\int_{{{1}}}^{{{3}}}}{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{x}{\sin{{y}}}{\left.{d}{y}\right.}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{{1}}}^{{{3}}}}{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{x}{\sin{{y}}}{\left.{d}{y}\right.}{\left.{d}{x}\right.}\)

asked 2021-08-09

Evaluate the following integrals. Include absolute values only when needed.

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\frac{{{\sin{{x}}}}}{{{1}+{\cos{{x}}}}}}{\left.{d}{x}\right.}\)

\(\displaystyle{\int_{{{0}}}^{{{\frac{{\pi}}{{{2}}}}}}}{\frac{{{\sin{{x}}}}}{{{1}+{\cos{{x}}}}}}{\left.{d}{x}\right.}\)

asked 2021-08-14

Evaluate the iterated integral.

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

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