# Evaluate Definite Integral Using Right Hand Rule: Show Work

• DemiMike
In summary, the conversation discusses using the definition of the definite integral with the right-hand rule to evaluate a given integral without using a shortcut method. The process involves using Riemann sums, specifically right-hand Riemann sums, to find the value of the integral. Some steps are shown, but the speaker is unsure of how to continue with the simplification.
DemiMike
Use the definiton of the definite inegral (with right hand rule) to evaluate the following integral. Show work please

Can NOT use shortcut method.. but be the long process

1
S (3x^2 - 5x - 6) dx
-4

edit:
i got this so far
1
S (3x^2 - 5x - 6) dx = [3x^3 /3 - 5x^2/2 - 6x], (1, -4)
-4
= 3*1/ 3 - 5*1 /2 - 6*1 - (3*4^3 - 5*4^2 - 6*2)

but iam lost in the simplification

edit: NVm i have no idea how to do the long method.. any 1 help <3 lpz

Last edited:
That looks like the 'shortcut' method, but it's not a bad idea to do that real quick to check yourself.

What you want to do (as per the directions) is evaluate it using Riemann sums. Specifically, right-hand Riemann sums.

## What is the "Evaluate Definite Integral Using Right Hand Rule" method?

The Evaluate Definite Integral Using Right Hand Rule method is a technique used to find the value of a definite integral by dividing the interval into small subintervals and approximating the area under the curve using rectangles with their right endpoints.

## Why is the "Evaluate Definite Integral Using Right Hand Rule" method useful?

The "Evaluate Definite Integral Using Right Hand Rule" method is useful because it provides an approximation of the value of a definite integral, which can be used in various real-life situations such as calculating areas or volumes.

## What is the process for using the "Evaluate Definite Integral Using Right Hand Rule" method?

The process for using the "Evaluate Definite Integral Using Right Hand Rule" method involves dividing the given interval into small subintervals, calculating the width of each subinterval, finding the right endpoint of each subinterval, and multiplying the width by the function value at the right endpoint. These values are then added together to give an approximation of the definite integral.

## How accurate is the "Evaluate Definite Integral Using Right Hand Rule" method?

The accuracy of the "Evaluate Definite Integral Using Right Hand Rule" method depends on the number of subintervals used. The more subintervals, the more accurate the approximation will be. However, it is still an approximation and may not give the exact value of the definite integral.

## Are there any limitations to the "Evaluate Definite Integral Using Right Hand Rule" method?

Yes, there are limitations to the "Evaluate Definite Integral Using Right Hand Rule" method. It cannot be used for all functions, especially those with complex curves. It also requires a significant amount of computation, making it time-consuming for large intervals.

• Calculus and Beyond Homework Help
Replies
10
Views
726
• Calculus and Beyond Homework Help
Replies
2
Views
588
• Calculus and Beyond Homework Help
Replies
18
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
630
• Calculus and Beyond Homework Help
Replies
1
Views
1K
• Calculus and Beyond Homework Help
Replies
5
Views
2K
• Calculus and Beyond Homework Help
Replies
2
Views
494
• Calculus and Beyond Homework Help
Replies
18
Views
4K
• Calculus and Beyond Homework Help
Replies
4
Views
1K