Why Is the Integral Result 175/3 Instead of 45?

  • Context: Undergrad 
  • Thread starter Thread starter homeworkhelpls
  • Start date Start date
  • Tags Tags
    Area Curve
Click For Summary

Discussion Overview

The discussion revolves around the evaluation of a definite integral, specifically why the result is 175/3 instead of 45, as calculated by some participants. The scope includes mathematical reasoning and potential errors in integration or limits.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • Some participants claim to have integrated the function to get 45, indicating a disagreement with the expected result of 175/3.
  • One participant suggests that the integral would yield 175/3 if the lower limit were x=-2, implying a possible error in the problem setup.
  • Another participant points out a potential notation issue with the expression (1/3)x^3, suggesting that it could be misinterpreted as 1/(3x^3), which may lead to confusion in calculations.

Areas of Agreement / Disagreement

Participants generally disagree on the correct result of the integral, with multiple competing views on the calculations and possible errors in the problem statement.

Contextual Notes

There may be limitations related to the assumptions about the limits of integration and the clarity of notation in the expression used for integration.

homeworkhelpls
Messages
41
Reaction score
1
1675365471735.png

i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
 
Last edited by a moderator:
Physics news on Phys.org
homeworkhelpls said:
View attachment 321610
i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
Both Wolfram Alpha and I agree with you.
 
Reply
  • Like
Likes   Reactions: homeworkhelpls and topsquark
Me too!
 
Reply
  • Like
Likes   Reactions: homeworkhelpls
The integral would evaluate to 175/3 if the lower limit were x=-2. I suspect a silly typo or calculation slip by the question setter.
 
Last edited:
Reply
  • Informative
  • Like
Likes   Reactions: homeworkhelpls and PeroK
homeworkhelpls said:
View attachment 321610
i integrated y to get (1/3x^3 + 2x) with upper limit 5 / lower limit 2 but got 45 not 175 / 3
Just a notation tip. 1/3x^3 can be misread as 1/(3x^3) placing the x^3 in the denominator. To be precise, we can instead write (1/3)x^3 to ensure x^3 is in the numerator and not mistakenly placed in the denominator.
 

Similar threads

Undergrad Different Substitution for Solving an Integral
  • · Replies 6 ·
Replies
6
Views
3K
High School Why is this definite integral a single number?
  • · Replies 20 ·
Replies
20
Views
4K
High School Calculating shaded area: I'm getting discrepancies between methods
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Result of this integral in large Lambda limit
  • · Replies 12 ·
Replies
12
Views
3K
MHB Calculate volume of a solid rotating around the y-axis
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Negative area above x-axis from integrating x^2?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Differentiability of a Multivariable function
  • · Replies 1 ·
Replies
1
Views
3K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K
High School Integration from "Area Under Curve" Perspective: Explained
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K