A pile of dirt is approximately in the shape of an inverted cone of height 4 m with a base radius...

Question:

A pile of dirt is approximately in the shape of an inverted cone of height 4 m with a base radius of 4 m. The density of the dirt is proportional to the distance from the apex of the pile of dirt. Set up an integral for the mass of the dirt pile.

Integral:

Integral is a technique in which we find the area, displacement, volume, etc by assigning a number to a function. The integral technique is just the opposite of differentiation technique. It means if we know the differentiation of any function then by going in reverse process or order we get the original function with an arbitrary constant.

Answer and Explanation:

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We have given that,

The density of the dirt is proportion to the distance from the open of the pile of the dirt .

Let us assume that,

{eq}h {/eq...

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Work as an Integral

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Chapter 7 / Lesson 9
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After watching this video, you will be able to solve calculus problems involving work and explain how that relates to the area under a force-displacement graph. A short quiz will follow.


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