Triangle Integral Formula: Uncovering the Truth Behind b3/6

  • Thread starter Thread starter robertjford80
  • Start date Start date
  • Tags Tags
    Integral Triangle
Click For Summary
SUMMARY

The discussion centers on the calculation of the area of a triangle using integration, specifically addressing the formula for the area, which is derived as b2/2. The integral of the triangle's area is correctly represented as b3/6, but this is a misunderstanding of the application of integration. For a triangle with a base of 4, the area calculated using the formula b2/2 results in an area of 8, confirming the correct application of the formula.

PREREQUISITES
  • Understanding of basic calculus concepts, particularly integration
  • Familiarity with geometric formulas for area calculation
  • Knowledge of the properties of triangles
  • Ability to interpret mathematical expressions and their applications
NEXT STEPS
  • Study the fundamentals of integration techniques in calculus
  • Explore the derivation of geometric area formulas
  • Learn about the application of definite integrals in calculating areas
  • Investigate common misconceptions in calculus related to area and volume
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in understanding the application of integration in geometric contexts.

robertjford80
Messages
388
Reaction score
0

Homework Statement



the formula of a triangle is b2/2, so the integral should be b3/6, right? Well, that can't be right. Because if the base of the triangle is 4, it's area will not add up to 8. What am I doing wrong?
 
Physics news on Phys.org
need more details about your problem to help.
 
The problem is find the area of a triangle with base 4 using integration.
 
(b^2)/2 is the area of the triangle - that's the formula you should get after you do the integration, not before. just think of integration as finding the area under the line
 
cool, thanks.
 

Similar threads

Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
1K
Calculating the area of equilateral triangle using calculus
  • · Replies 3 ·
Replies
3
Views
3K
Build right triangle with two points and a line
  • · Replies 7 ·
Replies
7
Views
2K
A line integral about a closed "unit triangle" around the origin
  • · Replies 12 ·
Replies
12
Views
4K
Why Do Different Integration Orders Give Different Results in Double Integrals?
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Fluid Force of Triangle Submerged in Water
  • · Replies 1 ·
Replies
1
Views
2K
Proving Vector Cross Product Properties in ℝ3?
  • · Replies 3 ·
Replies
3
Views
8K
Three principal axis moments of inertia for hexagonal prism?
  • · Replies 3 ·
Replies
3
Views
4K
Using series to prove hypothesis of right triangle's < limits
  • · Replies 9 ·
Replies
9
Views
2K
Sides of a triangle
  • · Replies 16 ·
Replies
16
Views
2K