Cracking The Ap Calculus ab Exam 2018

7.

If  we  let u   =    ,  then    du  =   − dx.   We  need    to  substitute  for  dx,    so  we  can divide  the du

term     by  −3:     −   dx.     Next    we  can     substitute  into    the     integral:  

. Now we can integrate: − (^) ∫ cos u du = − sin u + C.
Last, we substitute back and get

8. − cos (sin x) + C

If we let u = sin x, then du = cos x dx. Next we can substitute into the integral: ∫sin (sin x) cos

x dx = ∫sin u du. Now we can integrate: ∫sin u du = − cos u + C. Last, we substitute back and

get −   cos (sin    x)  +   C.

SOLUTIONS TO PRACTICE PROBLEM SET 20

1.

First,  let’s   draw    a   picture.