Download worksheet 4-2

Calculus AB
Section _________
Name: _______________________________
Date: _______________________________
~ 4-2 Approximate Area Under the Curve
1. Find the approximate area under the curve y  x 2 from [0,3] and n = 3 using the left-hand endpoint .
2. Find the approximate area under the curve y   x  1 from [-1,1] and n = 4 using the right-hand endpoint .
5
3. Find the approximate area under the curve y 
x 2  x  1 from [2, 10] and n = 4 using the midpoint.
4. Find the approximate area under the curve y 
x 1
from [2, 4] and n = 8 using the left-hand endpoint.
x 1
5. Find the approximate area under the curve y  4  x 2 from x = -1 to x = 1 using midpoint formula with n = 4
subintervals.
6. Find the approximate area under the curve y  2 x  x 2 from x = -1 to x = 2 using midpoint formula with n = 4
  3 
7. Find the approximate area under the curve y  sin( x)  2 on the domain  ,
with n = 4 subintervals
 2 2 
using right hand Riemann sums
8. Find the approximate area under the curve y  2 x  x 2 from x = 1 to x = 2 with n = 4 using Trapezoidal Rule.
9. Find the approximate area under the curve y  6  x 2 from x = 0 to x = 2 using Trapezoidal Rule with n = 4
subintervals.
10. Use the Trapezoidal Rule with 6 subintervals to approximate the area under the curve y 
1
on the
1 x2
interval [0, 6].
11. The table below gives data points for a continuous function. Approximate the area under the curve on the
interval [ 0, 2 ] using trapezoids and 10 equal subintervals.
x
f(x)
0
30
0.2
44
0.4
55
0.6
61
0.8
68
1.0
54
1.2
39
1.4
37
1.6
26
1.8
25
2.0
40
12. Approximate the area using the midpoint formula with 3 intervals of width 2 on the interval [ 0, 6]
x
f(x)
0
0
1
0.25
2
0.48
3
0.68
4
0.84
5
0.95
6
1