5 Steps to a 5 AP Calculus BC 2019

282 STEP 4. Review the Knowledge You Need to Score High

Step 2. Determine the radius of a disc from a cross section.

r= f(x)=

√

x− 1

Step 3. Set up an integral.

V=π

∫ 5

1

(f(x))^2 dx=π

∫ 5

1

(√

x− 1

) 2

dx

Step 4. Evaluate the integral.

V=π

∫ 5

1

(√

x− 1

) 2

dx=π[(x− 1 )]^51 =π

[

x^2

2

−x

] 5

1

=π

((

52

2

− 5

)

−

(

12

2

− 1

))

= 8 π

Verify your result with a calculator.

Example 2

Find the volume of the solid generated by revolving about thex-axis the region bounded by

the graph ofy=

√

cosxwhere 0≤x≤

π

2

, thex-axis, and they-axis.

Step 1. Draw a sketch. (See Figure 12.4-8.)

y

x

y =

0

1

2

√cos x

π

Figure 12.4-8

Step 2. Determine the radius from a cross section.

r= f(x)=

√

cosx

Step 3. Set up an integral.

V=π

∫π/ 2

0

(√

cosx

) 2

dx=π

∫π/ 2

0

cosxdx