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Problem 565

Express $\mathrm{x} \int_{0} \sqrt{\left(1-4 \sin ^{2} \mathrm{u}\right) \text { du in terms of incomplete elliptic }}\( integrals where \)0 \leq \mathrm{x} \leq(\pi / 6)$.

Expert verified

The given integral can be expressed in terms of an incomplete elliptic integral of the second kind as \[\mathrm{x} E(\mathrm{u}, 2), \quad 0 \leq \mathrm{u} \leq (\pi / 6).\]

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Chapter 19

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Chapter 19

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Chapter 19

Express $\mathrm{x} \int_{0} \sqrt{\left(1-4 \sin ^{2} \mathrm{u}\right) \text { du in terms of incomplete elliptic }}\( integrals where \)0 \leq \mathrm{x} \leq(\pi / 6)$.

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