Barrons AP Calculus

AB/BC 3.

(b)

(c)

AB/BC 4.

Part B

(a) ΔA  =   (g(x)   −   f(x)    )   Δx, so:

Let h   =   the hypotenuse  of  an  isosceles   right   triangle,   as  shown

in  the figure. Then    each    leg of  the triangle    is      and

its area    is  

An  element of  volume  is

and thus    .

Washers;        where:

r 1     =   3   −   f(x)    =   3   −   (cos    πx  −   1),

r 2     =   3   −   g   (x) =   3   −   x(2 −   1).

So  .

(a)  ,  so  v(0)    =   0   and v(10)   =   48.