How Do You Calculate the Volume of a Solid Revolved Around the X-Axis?

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In summary, the problem involves finding the volume of a solid generated by revolving a triangular region in the first quadrant bounded by the x-axis, the line x=PI/3, and the curve y=tanx about the x-axis. The volume can be calculated using the disk, shell, or washer method, but the problem may become complicated when trying to express the line x=pi/3 in numbers. It is important to carefully sketch the given shapes and determine the function r(x) for the integral.
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Theorotical
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Homework Statement


Fine the volume of the solid generated by revolving the "triangular" region bounded by the x-axis, the line x=PI/3, and the curve y=tanx in the first quadrant about the x-axis.


Homework Equations



volume of revolution using disk method =integration (PI*[r(x)]squared dx) also using the shell and washer method

The Attempt at a Solution


i have tried to sketch but the problem is how to express the line PI/3 in numbers, also when i integrate using the following method:
V=int.[from 0 to root 3][PI*(root 3 -tanx)squared] dx

the problem gets more complicated and i feel frustrated as my exam is tom. and am really scared from these kind of problems, so please help me
 
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  • #2
Where did 'root 3' come from? x=pi/3 is a vertical line through (pi/3,0). The x-axis is a horizontal line through (0,0). y=tan(x) is a curve connecting (0,0) and (pi/3,tan(pi/3)). Draw them. You are integrating along x. What is r(x) as a function of x?
 

FAQ: How Do You Calculate the Volume of a Solid Revolved Around the X-Axis?

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