Question

What kind of question will ask us to use this type of format to evaluate the integral instead of doing the regular integral evaluation?

Answer 1

Great work!

Explanation:

These kind of questions are calculated through Riemann Sum. You can evaluate any definite integral using the Riemann Sum. It should be in the following form:

f(x)dx on the interval [a, b], or

`\int _a^b\:f\left(x\right)dx`

Now f(x) is simply y. Therefore in this example y = x^3 - 6x. We just need the sufficient amount of data to apply the Riemann Sum, including the interval [a, b] that bounds the area, and the the number of rectangles 'n' that we need to use.

Consider an easier approach to this question: (First attachment)

Graph: (Second Attachment)