How to solve (e) and (f)

[helpmath00]

 

[Deleted member 4993]

View attachment 12153

For (e), substitute

u = x -1

Don't forget to change the limits of integration after substitution.

 

[helpmath00]

For (e), substitute

u = x -1

Don't forget to change the limits of integration after substitution.

It should be the same answer as (a) right?

 

[HallsofIvy]

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), $\displaystyle [f(x)]^2= 1- (x-1)^2= 2x- x^2$.