May 17th, 2019, 08:42 AM  #1 
Member Joined: Oct 2012 Posts: 78 Thanks: 0  integration
Hi How we can get integral of f(x)=(9x^2)^(1/2) without using trigonometric substitution. indefenite integral. 
May 17th, 2019, 08:57 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,926 Thanks: 2205 
The hint I gave you for the definite integral can also be applied to obtain an indefinite integral.

May 17th, 2019, 02:37 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,806 Thanks: 716 
The graph of the function is a semicircle of radius 3 centered at (3,0). To get an indefinite integral calculate the angle between the x value on the circle and add the sector area to the triangle area (for x > 3). If x < 3, you need to subtract a triangle from the sector area.
Last edited by mathman; May 17th, 2019 at 02:42 PM. 

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