# 3. Although we usually assume a uniform partition when performing numerical integration, there are occasions where a non-uniform partition might be more useful. For example, consider the integral 01x+12dx.Show the partition {0.00,0.21,0.44,0.69,0.96,1.00} gives Riemann sums where a calculator is not needed to find the values of f(xi), except for the final value which is just the square root of 2.Calculate the left and right Riemann sums and average them, which thus gives the result of the trapezoidal rule with a non-uniform partition. If you wanted to do a similar calculation which provided more accuracy, what new partition could you use? (Hint: consider the perfect squares which lie between 1000 and 2000.)