Question

Need help evaluating this integral(posted in first response)

Answer 1

\[\int\limits_{0}^{1}t \sqrt{1-t}\]

Answer 2

u = 1-t --> t = 1-u
du = -dt --> dt = -du
\[\int\limits_{0}^{1}\sqrt{u}(1-u) du\]
distribute
\[\int\limits_{0}^{1}(\sqrt{u} -u \sqrt{u}) du\]
rewrite using exponents
\[\int\limits_{0}^{1}u^{1/2}-u^{3/2} du\]
then integrate each term separately