December 4, 2012AIM: What is the difference between the Mean Value and Average Value? How do we use u-substitution to find integrals?

DO NOW:

HW4.4c Pg. 291 – 292 #43 – 46, 48; Pg. 91 # 11 – 21 odd

f (x) 2x 3 3x 2 12x

3. Find the relative minimum of f(x)

limx 4

f (x)

f (x)

limx 2

f (x)a) b)

1. 2. Find f if f’(x)=5x4 – 2x5 and f(0) = 4.

MVT vs Average Value for Integrals

• Mean Value Theorem for Integrals

• Definition of an average value of a function on an interval

Calculus in Motion - MVT

How would I find this integral?

CxuFdxxuxuf ))(()('))((U-Substitution

Steps for using u-substitution!

1. Determine what u = and du =.2. Substitute u and du into your

integrand.3. Now, integrate your integrand with

respect to u.4. Finally, change everything back to

the variable x and don’t forget your +C!

CxuFdxxuxuf ))(()('))((U-Substitution

Example 2

dx

x

x32 )1(

2

Example 3

2x(x 2 9)5dx

How do I figure out what the “u” is?

3x

dx

sin2 x cos xdx

3x 2 sin(x 3)dx

2x(x 2 9)4 dx

Example 4

(tan x)dx

Classwork

dxxx

x32 )(

12.1 dxxx ))(cos(sin.2 3

3. If f(x) =

and f(1) = 2, find f(x) dxxx )32( 2