5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 16:1

Areas and Volumes 285

∫k

0

sinxdx= 2

∫π

k

sinxdx

−cosx]k 0 = 2 [−cosx]πk

−cosk−(−cos(0))= 2 (−cosπ−(−cosk))

−cosk+ 1 =2(1+cosk)

−cosk+ 1 = 2 +2 cosk

−3 cosk= 1

cosk=−

1

3

k=arc cos

(

−

1

3

)

= 1. 91063

Area Between Two Curves

Area Bounded by Two Curves. (See Figure 13.3-8.)

a 0 bc d

f

y

g

x

Figure 13.3-8

Area=

∫c

a

[f(x)−g(x)]dx+

∫d

c

[g(x)− f(x)]dx.

Area=

∫d

a

(upper curve−lower curve)dx.