Solving Calculus Homework: Stuck on #11 Riemann's Sum

In summary, the student is struggling with problem number 11 on their homework and believes it has something to do with Riemann's Sum. They have attempted to start by putting numbers in for p, but are unsure if this is correct. The conversation then transitions to discussing the definition of a Riemann sum and how it applies to the function ##x^p##. The student is asked to consider dividing the interval from 0 to 2 into equal subintervals and to try the cases of 2, 3, and 4 subintervals to better understand the concept.
  • #1
KF33
19
0

Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.
 

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  • #2
KF33 said:

Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.
Could you please show us a) what's written on number 11, as your picture is unreadable without processing it further, and b) what you have done so far and why?
 
  • #3
Screen Shot 2019-01-24 at 6.04.34 PM.png
 

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  • #4
KF33 said:

Homework Statement


I am stuck on number 11 on my homework.

Homework Equations


Not Sure

The Attempt at a Solution


I know this has to have something to do with Riemann's Sum, but I am lost on where to start. I started by putting numbers in for p, but I think that is wrong.

What is the definition of a Riemann sum? For the function ##x^p##, what would be a Riemann sum for ##\int_0^2 x^p \, dx## if you were to divide the interval from ##x=0## to ##x = 2## into ##n## equal-sized subintervals?

To fix in your mind what is going on, try first the simple cases of ##n = 2, n = 3## and ##n = 4## subintervals.
 

1. What is Riemann's Sum?

Riemann's Sum is a method used in calculus to approximate the area under a curve by dividing it into smaller rectangles and summing up their areas.

2. How do I know if I am stuck on #11 Riemann's Sum?

If you are solving a calculus homework problem and it specifically mentions Riemann's Sum in question #11, then you are stuck on #11 Riemann's Sum.

3. What is the process for solving #11 Riemann's Sum?

The process for solving #11 Riemann's Sum involves determining the width of each rectangle, calculating the height of each rectangle using the given function, and then summing up the areas of all the rectangles to approximate the area under the curve.

4. What are some common mistakes to avoid when solving #11 Riemann's Sum?

Some common mistakes to avoid when solving #11 Riemann's Sum include using the wrong function or interval, miscalculating the width or height of the rectangles, and forgetting to include all the rectangles in the sum.

5. How can I check my answer for #11 Riemann's Sum?

You can check your answer for #11 Riemann's Sum by using a calculator or graphing software to graph the function and the rectangles, and comparing the approximate area under the curve to the actual area under the curve.

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