Triangle Integral Formula: Uncovering the Truth Behind b3/6

In summary, the Triangle Integral Formula is a mathematical equation used to calculate the area of a triangle using its base and height. It is derived using the concept of integration and is commonly written as A = 1/2 * b * h. The b3/6 term in the formula is a constant value that helps with accuracy, and the formula can be used for all types of triangles. It has practical applications in fields such as engineering, architecture, and physics.
  • #1
robertjford80
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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?
 
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  • #3
The problem is find the area of a triangle with base 4 using integration.
 
  • #4
(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
 
  • #5
cool, thanks.
 

FAQ: Triangle Integral Formula: Uncovering the Truth Behind b3/6

What is the Triangle Integral Formula?

The Triangle Integral Formula is a mathematical equation that calculates the area of a triangle using its base and height. It is commonly written as A = 1/2 * b * h, where A represents the area, b represents the base, and h represents the height.

How is the Triangle Integral Formula derived?

The Triangle Integral Formula is derived using the concept of integration, which is a fundamental concept in calculus. By splitting a triangle into infinitely small rectangles and summing their areas, we can arrive at the formula A = 1/2 * b * h.

What is the significance of b3/6 in the Triangle Integral Formula?

The b3/6 term in the formula is a result of integrating the function that represents the area of a triangle. It is a constant value that helps to accurately calculate the area of a triangle using the base and height.

Can the Triangle Integral Formula be used for all types of triangles?

Yes, the Triangle Integral Formula can be used for all types of triangles, including equilateral, isosceles, and scalene triangles. As long as the base and height are known, the formula can be used to calculate the area.

How is the Triangle Integral Formula useful in real-life applications?

The Triangle Integral Formula is useful in various fields such as engineering, architecture, and physics. It allows us to accurately calculate the area of triangles, which is essential in designing structures and solving real-life problems involving triangles.

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