Find Volume of Revolution by Integrating 1/sqroot(3x+2) around x=0 and x=2

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SUMMARY

The discussion focuses on calculating the volume of revolution for the function y = 1/sqrt(3x + 2) when rotated around the x-axis between the limits x = 0 and x = 2. The formula used is V = π∫(y^2)dx, leading to the integral π∫(1/(3x + 2))dx. A substitution method is suggested, specifically u = 3x + 2, to simplify the integration process. The user seeks clarification on the integration process and the constant involved in the natural logarithm.

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  • Knowledge of substitution methods in integration
  • Basic proficiency in handling logarithmic functions
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  • Learn about the volume of solids of revolution using the disk method
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DeanBH
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so i have y = 1/sqroot(3x+2)

find volume when rotated around x, regions are x=2 and x=0



equation needed: V= integral Pi*y^2*dx

so.

i do intergral pi* (1/sqroot(3x+2))^2 * dx

so i get pi integral 1/(3x+2) dx

so how do i integrate 1/sqroot(3x+2) ?

can someone take me though it , because i know there's meant to be a constant near the ln, but i don't know how to find it.


thanks, sorry if it's explained bad
 
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Try putting u=3x+2
 

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