1. Approximation and Computing Area
AP Calculus 5-1
Approximation and Computing
Area

2. 𝑦= 𝑥 2 𝑜𝑛 0,4

3. Right-Endpoint Approximation
With N intervals find the area under the curve 4
f(x)
Area 16 64 2
f(x)
Area 4 8 16 32 1
f(x)
Area 2 4 3 9 16

4. f(x)
Area
1/16
1/64
9/16
9/64 1
5/4
25/16
25/64
3/2
9/4
7/4
49/16
49/64 2 4
81/16
81/64
5/2
25/4
11/4
121/16
121/64 3 9
13/4
169/16
169/64
7/2
49/4
15/4
225/16
225/64 16

5. Left-Endpoint Approximation
With N intervals find the area under the curve 4
f(x)
Area 2
f(x)
Area 4 8 1
f(x)
Area 2 4 3 9

6. Mid-Point Approximation
With N intervals find the area under the curve 4
f(x)
Area 2 16 2
f(x)
Area 1 3 9 18 1
f(x)
Area
3/2
9/4
5/2
25/4
7/2
49/4

8. 𝑓 𝑥 increasing 𝑓(𝑥) decreasing 𝐿 𝑁 ≤𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑐𝑢𝑟𝑣𝑒≤ 𝑅 𝑁
𝑅 𝑁 ≤𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑐𝑢𝑟𝑣𝑒≤ 𝐿 𝑁

9. 𝐿 6 , 𝑓 𝑥 = 6𝑥+2 , 1,3 ∆𝑥= 3−1 6 = 1 3 7.1463 x f(x) Area 1 2.828
𝐿 6 , 𝑓 𝑥 = 6𝑥+2 , 1,3
∆𝑥= 3−1 6 = x
f(x)
Area 1
2.828
0.9428
4/3
3.1622
1.0541
5/3
3.4641
1.1547 2
3.7417
1.2472
7/3 4
1.3333
8/3
4.2426
1.4142

10. Problems
5-1 Page 296 #1-12, odd