Triangle Integral Formula: Uncovering the Truth Behind b3/6

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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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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