Please help me with this question!

Question

Write the definite integral for the summation: 

Options:

1. 
2. 
3. 
4. 

Answer 1

Hi Zayn C.,

I think you want more here than just to be handed the answer, you want the power to analyse the problem and figure out the answer yourself??

So -- for these kinds of problems, you are looking for various kinds of clues. But the first one, and the only one you need here, is to transform the expression into its values at the limits of the summation. So -- at the high end for k, (2+(n/n))^3 * (1/n), and at the bottom, (2 + (1/n))^3 * (1/n) .

The first of these translates into (2+1)^3 , or 3^3 , times a "slicing" term of (1/n), and the second of these translates into (2+0)^3, or 2^3, times the "slicing" term (by which, I mean that you have n slices, so each one is naturally enough (1/n) thickness, like slicing a pickle lengthwise into n slices!

So right away, you see that the x^3 is the argument you want, and over the 2 to 3 interval. i.e. choice (2).

-- Cheers, -- Mr. d.

Answer 2

This sum is right integral sum for function f(x) = x³, interval [2, 3] and n subdivisions.

Because answer is 2).