Please can you help me with this question?

Question

Compute the following Riemann sums of the function on the interval .

..............., ................. , ..................

............., ............., .................

............, ............ , .................

Make an educated guess of the exact area bounded by and the -axis on the interval .

Exact Area = ..................

Answer 1

This is not a hard problem, just a tedious problem.

Here is a sketch of L₅

You divide the space between 1 and 4 into 5 even increments, so each would be (4 - 1)/5 = 0.6 wide.

You find the function values at the left side of each rectangle (the height of each rectangle) and multiply them by the width (0.6):

f(1)•0.6 + f(1.6)•0.6 + f(2.2)•0.6 + f(2.8)•0.6 + f(3.4)•0.6

Then repeat for the midpoint to get M₅:

f(1.3)•0.6 + f(1.9)•0.6 + f(2.5)•0.6 + f(3.1)•0.6 + f(3.7)•0.6

Then repeat for the right side to get R₅:

f(1.6)•0.6 + f(2.3)•0.6 + f(2.8)•0.6 + f(3.4)•0.6 + f(4)•0.6

You can use your TI-84 to do this by putting the function in your Y1 and then using the function value "button" however, the easiest way is to use Excel.