Finding volume using integration

Thread starter ver_mathstats
Start date Nov 23, 2019
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Integration Volume

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The discussion centers on calculating volume using integration, specifically the formula for volume as the definite integral of the cross-sectional area A(x). The user attempted to find the volume by integrating ∫4x^2dx from 0 to 5 and arrived at an answer of 500/3, which was deemed incorrect. A key point raised is that the user mistakenly integrated the height instead of the area. This highlights the importance of correctly identifying the function being integrated to obtain the correct volume. Understanding the distinction between area and height is crucial for accurate volume calculations.

Nov 23, 2019

ver_mathstats

Homework Statement: The base of the solid is a square, one of whose sides is the interval [0,5] along the the x-axis.
The cross sections perpendicular to the x-axis are rectangles of height f(x)=4x^2. Compute the volume of the solid.

Relevant Equations: f(x)=4x^2

I know that the formula for volume is equal to the definite integral ∫A(x)dx, where A(x) is the cross sectional. I found the definite integral where b=5 and a=0, for ∫4x²dx. I obtained the answer 500/3, however this was incorrect, and I'm unsure of where I went wrong?

Thank you.

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Nov 23, 2019

Orodruin

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You have not integrated the area, you have integrated the height.

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