S Subhotosh Khan Super Moderator Staff member Joined Jun 18, 2007 Messages 18,246 May 16, 2019 #2 helpmath00 said: View attachment 12153 Click to expand... For (e), substitute u = x -1 Don't forget to change the limits of integration after substitution.

helpmath00 said: View attachment 12153 Click to expand... For (e), substitute u = x -1 Don't forget to change the limits of integration after substitution.

H helpmath00 New member Joined May 16, 2019 Messages 2 May 16, 2019 #3 Subhotosh Khan said: For (e), substitute u = x -1 Don't forget to change the limits of integration after substitution. Click to expand... It should be the same answer as (a) right?

Subhotosh Khan said: For (e), substitute u = x -1 Don't forget to change the limits of integration after substitution. Click to expand... It should be the same answer as (a) right?

H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 4,946 May 16, 2019 #4 The equation of a circle, with center at (1, 0) and radius 1 is \(\displaystyle (x- 1)^2+ y^2= 1\). The semi-circle above the x-axis is given by \(\displaystyle y= \sqrt{1- (x- 1)^2}\). So for (f), \(\displaystyle [f(x)]^2= 1- (x-1)^2= 2x- x^2\).

The equation of a circle, with center at (1, 0) and radius 1 is \(\displaystyle (x- 1)^2+ y^2= 1\). The semi-circle above the x-axis is given by \(\displaystyle y= \sqrt{1- (x- 1)^2}\). So for (f), \(\displaystyle [f(x)]^2= 1- (x-1)^2= 2x- x^2\).