This problem differs from the others in the set, in that the sub$-$intervals used for the widths of the rectangles are not all the same width. That is$,$ the partition is "non$-$uniform".

Approximate ${\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}xsin(x)dx$ by computing the Left and Right sums, using the partition $\{0,\frac{}{6},\frac{}{4},\frac{}{3},\frac{}{2}\}.$

Your answers should be accurate to at least $6$ decimal places.

Left Sum $=$

Right Sum $=$

You may include a formula as an answer.