Finding Volume by Rotating Curves around the x-axis

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SUMMARY

The discussion focuses on calculating the volume of a solid formed by rotating the region bounded by the curves y = 6x², y = 0, and x = 1 around the x-axis. The correct formula to use is V = π∫[0 to 1] (6x²)² dx, which simplifies to V = π∫[0 to 1] 36x⁴ dx. The user initially misapplied the integration limits and the formula, leading to confusion, but later recognized the error and acknowledged the need for rest.

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Homework Statement



Find the volume of the solid made by rotating the region bounded by the given curves around the x-axis.

y = 6x2, y = 0, and x = 1

Homework Equations



V= A(x)*h where h = dx

The Attempt at a Solution



As I was taught in class, I tried using 6x2 as my radius, squaring it, and multiplying it by π, and integrating it (using dx as height of course). The lower limit of integration is 0, as given by the line y=0. The upper limit would need to be the value of y when x=1, which is 6. So, [itex]\int[/itex]36∏x^4 dx with the limits mentioned is what i get for my answer, however I am apparently wrong. What did I do wrong?

EDIT: Never mind, I see the dumb mistake I made in approaching this... it's time for me to go to bed, I've done nothing but study today and I probably need rest. Mods can delete if need be.
 
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Well done :)
 

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