Cracking The Ap Calculus ab Exam 2018

10.

To  find    the volume  of  a   solid   with    a   cross-section   of  a   square, we  integrate   the area    of  the

isosceles   right   triangle        over    the endpoints   of  the interval.   Here,   the hypotenuses

of  the triangles   are found   by  f(x)    −   g(x)    =   4   −   x^2 ,   and the intervals   are found   by  setting y   =   x^2

equal   to  y   =   4.  We  get x   =   −2  and x   =   2.  Thus,   we  find    the volume  by  evaluating  the integral    

=    =   .   We  get    

= = .

SOLUTIONS TO PRACTICE PROBLEM SET 26

1.

We  solve   this    differential    equation    by  separation  of  variables.  We  want    to  get all of  the y

variables   on  one side    of  the equals  sign    and all of  the x   variables   on  the other   side.   We  can do

this    easily  by  cross-multiplying.  We  get y^3 dy  =   7x^2 dx.    Next,   we  integrate   both    sides.

∫^ y

(^3) dy =

∫^7 x

(^2) dx
y^4 = + C
Now we solve for C. We plug in x = 3 and y = 2.
16 = 252 + C
C = −236