Definite Integration

Using the substitution x=\sin^{2}{\theta}, evaluate:

    \[\int_{0}^{1} \sqrt{x}\sqrt{1-x}\,\textrm{d}\theta\]

Source:

Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Examples 17b: Question 40, p. 230)

Solution:

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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