1. Applications of integration
Group 1

2. Rectangular approximation

3. • LRAM
▫ From the left
• MRAM
▫ From the middle
• RRAM
▫ From the right

4. Summation Notation

5. 

n
k
nck
1



n
k
nn
k
1 2
)1(



n
k
nnn
k
1
2
6
)12)(1( 2
1
3
2
)1(





 

nn
k
n
k

6. Area Methods

7. • X-axis
• Y-axis
• Inverse
• Area Between 2 Curves

8. Volume Methods

9. • Washer
• Disk
• Shell
dxbottomtop
r
l
)( 22

Disk
dxbottomtop
r
l
)( 
dxrwh
r
l
)(2 

10. Properties of integrals

11. • Constant property (put constant in front)
• Bounds property (flip the start and end
values and add a negative)
• Integral sum property (splip up f(x) and
g(x) into two separate integrals)