Question

Numerical Approximation Methods with Integrals - 12th Grade Calculus Please help me, thanks!

Answer 1

Step 1:

The lower sum is the sum over the 4 partitions of the

`\text{Product of the }\frac{(b\text{ - a)}}{4}\text{ }*\text{ f( lower bound )}`

Step 2:

The upper sum is the sum over the 4 partitions of the

`\text{Product of the }\frac{(b\text{ - a)}}{4}\text{ }*\text{ f( upper bound )}`

Step 3:

Trapezoid rule will take the line that joins the upper and the lower values in each partition ( average of the upper and lower) , resulting in a sum that is between the upper sum and the lower sum.

Final answer

Lower sum < trapezoid rule < upper sum