Express the given integral as the limit of a riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.

We will use the right Riemann sum. We can break this integral in two parts.

We take the interval and we divide it n times:

The area of the i-th rectangle in the right Riemann sum is:

For the first part of our integral we have:

For the second part we have:

We can now put it all together:

We can also write n-th partial sum:

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.