Cracking The Ap Calculus ab Exam 2018

Step    4:  Substituting    back,   we  get     +   C.

31. C These are a pair of basic trigonometric integrals. You should have memorized several

trigonometric integrals, particularly ∫ sin x dx = −cos x + C and ∫cos x dx = sin x + C.

Step    1:  sin x   dx  +       cos x   dx  =   −   cos     +   sin 

Step    2:  Now we  evaluate    the limits  of  integration,    and we’re   done.

32. A Step 1: The boats are moving at right angles to each other and are thus forming a right triangle
    with the distance between them forming the hypotenuse.

Whenever    we  see right   triangles   in  related rates   problems    we  look    to  use the Pythagorean

Theorem.    Call    the distance    that    Boat    A   travels y   and the distance    that    Boat    B   travels x.  Then

the rate    at  which   Boat    A   goes    north   is   ,  and the rate    at  which   Boat    B   travels is   .  The

distance    between the two boats   is  z,  and we  are looking for how fast    z   is  growing,    which   is  

. Now use the Pythagorean Theorem to set up the relationship: x^2 + y^2 = z^2.

Step    2:  Differentiating both    sides   we  obtain

Step    3:  After   2.5 hours,  Boat    A   has traveled    30  km  and Boat    B   has traveled    45  km. Because of